We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the tran...We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the transversefield Ising model(TFIM)as a case study,we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates.Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition,as reflected in the behavior of specific componentsξ_(i)^((k))within the eigen microstates.This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.展开更多
Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning me...Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy,correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high e?ciency method and use it to calculate entanglement entropy(EE) of the system and get results consistent with previous work very well.展开更多
Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We ...Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We begin with the transverse field Ising chain(TFIC)at quantum critical point and examine how it evolves under perturbations,such as an applied longitudinal field or weak coupling to another quantum critical TFIC.展开更多
Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scali...Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scaling and universality,the former has recently also been demonstrated to exhibit scaling and universal behavior within a mesoscopic,coarse-grained Landau-Ginzburg theory.Here we apply this theory to a microscopic model-the paradigmatic Ising model,which undergoes FOPTs between two ordered phases below its critical temperature-and unambiguously demonstrate universal scaling behavior in such FOPTs.These results open the door for extending the theory to other microscopic FOPT systems and experimentally testing them to systematically uncover their scaling and universal behavior.展开更多
Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to ver...Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.展开更多
We have studied the nucleation process of a two-dimensional kinetic Ising model subject to a bias oscillating external field, focusing on how the nucleation time depends on the oscillation frequency. It is found that ...We have studied the nucleation process of a two-dimensional kinetic Ising model subject to a bias oscillating external field, focusing on how the nucleation time depends on the oscillation frequency. It is found that the nucleation time shows a clear-cut minimum with the variation of oscillation frequency, wherein the average size of the critical nuclei is the smallest, indicating that an oscillating external field with an optimal frequency can be much more favorable to the nucleation process than a constant field. We have also investigated the effect of the initial phase of the external field, which helps to illustrate the occurrence of such an interesting finding.展开更多
Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavor- able circumstance an agent also has a possibility of holding its own state and reselecting its neighb...Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavor- able circumstance an agent also has a possibility of holding its own state and reselecting its neighbors. To describe this kind of phenomena an Ising model on evolution networks was presented and used for consensus formation and separation of opinion groups in human population. In this model the state-holding probability p and selection-rewiring probability q were introduced. The influence of this mixed dynamics of spin flips and network rewiring on the ordering behavior of the model was investigated, p hinders ordering of opinion networks and q accelerates the dynamical process of networks. Influence of q on the ordering and separating stems from its effect on average path length of networks.展开更多
A decorated lattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regul...A decorated lattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-nelghbor, and four-spin interactions, and the critical fixed point is found at K1 = 0.5769, K2= -0.0671, and K3 = 0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.展开更多
An overview of the mathematical structure of the three-dimensional（3D） Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D I...An overview of the mathematical structure of the three-dimensional（3D） Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D Ising model,Reidemeister moves in the knot theory,Yang-Baxter and tetrahedron equations,the following facts are illustrated for the 3D Ising model.1） The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a（3＋1）-dimensional space-time as a relativistic quantum statistical mechanics model,which is consistent with the 4-fold integrand of the partition function obtained by taking the time average.2） A unitary transformation with a matrix that is a spin representation in 2 n·l·o-space corresponds to a rotation in 2n·l·o-space,which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model.3） A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model,and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures.4） The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases φx,φy,and φz.The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail.The conjectured exact solution is compared with numerical results,and the singularities at/near infinite temperature are inspected.The analyticity in β=1/（kBT） of both the hard-core and the Ising models has been proved only for β〉0,not for β=0.Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.展开更多
In this work,the computational complexity of a spin-glass three-dimensional(3D)Ising model(for the lattice sizeN=lmn,wherel,m,n are thenumbersof lattice points along three crystallographic directions)is studied.We pro...In this work,the computational complexity of a spin-glass three-dimensional(3D)Ising model(for the lattice sizeN=lmn,wherel,m,n are thenumbersof lattice points along three crystallographic directions)is studied.We prove that an absolute minimum core(AMC)model consisting of a spin-glass 2D Ising model interacting with its nearest neighboring plane,has its computational complexity O(2mn).Any algorithms to make the model smaller(or simpler)than the AMC model will cut the basic element of the spin-glass 3D Ising model and lost many important information of the original model.Therefore,the computational complexity of the spin-glass 3D Ising model cannot be reduced to be less than O(2mn)by any algorithms,which is in subexponential time,superpolynomial.展开更多
The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and th...The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/ zJ-longitudinal crystal D / zJ field plane. We find that there are the first order-order phase transitions in a very small range of D /zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions,展开更多
The review paper by Zhang Zhi-Dong （Zhang Z D 2013 Chin. Phys. B 22 030513, arXiv：1305.2956） contains many errors and is based on several earlier works that are equally wrong.
We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined ...We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L=8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Тc=3.6403（2）. A convincing finite-size scaling analysis of the model yields ν=0.9995（21）, β/ν=0.12400（17）, γ/v=1.75223（22）, γ^1/ν=1.7555（22）, α/ν=0.00077（420） （scaling） and α/ν=0.0010（42） （hyperscaling）. The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.展开更多
An improved transverse Ising model is proposed by taking the depolarization field effect into account. Within the framework of mean-held theory we investigate the behavior of the ferroelectric thin film. Our results s...An improved transverse Ising model is proposed by taking the depolarization field effect into account. Within the framework of mean-held theory we investigate the behavior of the ferroelectric thin film. Our results show that the influence of the depolarization field is to flatten the spontaneous polarization profile and make the films more homogeneous, which is consistent with Ginzburg Landau theory. This fact shows that this model can be taken as an effective model to deal with the ferroelectric film and can be further extended to refer to quantum effect. The competition between quantum effect and depolarization field induces some interesting phenomena on ferroelectric thin films.展开更多
Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an e...Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory （EFT） and a mean-field theory （MFT）. The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shiet al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency （w） and static external field amplitude （h0） for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of w and h0.展开更多
The effect of electron itineracy on the magnetism of S＝1/2 ferromagnetic Ising model is investigated by introducing a hopping term. The electron Green's function method is used to deal with this Hamiltonian. Here...The effect of electron itineracy on the magnetism of S＝1/2 ferromagnetic Ising model is investigated by introducing a hopping term. The electron Green's function method is used to deal with this Hamiltonian. Here emphasis is made on that the magnetization is caused by the difference between the filling of spin-up and spin-down electrons.This concept is in accordance with that of band structure theory. In the zero band width limit, our results are the same as obtained by spin Green's function method. However, our method achieves more detailed physical information. The spontaneous magnetization, Curie temperature, total energy, and specific heat are calculated and investigated in detail by the densities of states. Hopping term depresses the Curie temperature but remains the order-disorder transformation still to be second order transition. Above the transition point, the energy band is the same as that of tight binding system because exchange interaction has no effect anymore. While under the transition point, the energy band splits into two subbands due to exchange interaction.展开更多
The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory(EFT)with correlations.The temperature effects on the pseudo-spin ...The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory(EFT)with correlations.The temperature effects on the pseudo-spin systems are unveiled in three-dimensional(3-D)and two-dimensional(2-D)phase diagrams.Moreover,the dynamic behaviors of exchange interactions on the 3-D and 2-D phase transitions under high temperature are exhibited.The results present that it is hard to obtain pure ferroelectric phase under high temperature;that is,the vibration of orderly pseudo-spins cannot be eliminated completely.展开更多
The time evolution of the Hamming distance (damage spreading) for the and Ising models on the square lattice is performed with a special metropolis dynamics algorithm. Two distinct regimes are observed according to ...The time evolution of the Hamming distance (damage spreading) for the and Ising models on the square lattice is performed with a special metropolis dynamics algorithm. Two distinct regimes are observed according to the temperature range for both models: a low-temperature one where the distance in the long-time limit is finite and seems not to depend on the initial distance and the system size; a high-temperature one where the distance vanishes in the long-time limit. Using the finite size scaling method, the dynamical phase transition (damage spreading transition) temperature is obtained as for the Ising model.展开更多
We use the quantum renormalization-group（QRG） method to study the entanglement and quantum phase transition（QPT） in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys....We use the quantum renormalization-group（QRG） method to study the entanglement and quantum phase transition（QPT） in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.（N.Y.） 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12475033,12135003,12174194,and 12405032)the National Key Research and Development Program of China(Grant No.2023YFE0109000)+1 种基金supported by the Fundamental Research Funds for the Central Universitiessupport from the China Postdoctoral Science Foundation(Grant No.2023M730299).
文摘We propose an eigen microstate approach(EMA)for analyzing quantum phase transitions in quantum many-body systems,introducing a novel framework that does not require prior knowledge of an order parameter.Using the transversefield Ising model(TFIM)as a case study,we demonstrate the effectiveness of EMA by identifying key features of the phase transition through the scaling behavior of eigenvalues and the structure of associated eigen microstates.Our results reveal substantial changes in the ground state of the TFIM as it undergoes a phase transition,as reflected in the behavior of specific componentsξ_(i)^((k))within the eigen microstates.This method is expected to be applicable to other quantum systems where predefining an order parameter is challenging.
基金Supported by the Natural Science Foundation of China under Grant No.11875082
文摘Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355(2017) 602], we construct the neural-network quantum state of transverse-field Ising model(TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration(SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy,correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high e?ciency method and use it to calculate entanglement entropy(EE) of the system and get results consistent with previous work very well.
基金supported by the National Natural Science Foundation of China Grant Nos.12450004,12274288the Innovation Program for Quantum Science and Technology Grant No.2021ZD0301900。
文摘Quantum integrability provides a unique and powerful framework for accurately understanding quantum magnetism.In this review,we focus specifically on several quantum integrable low-dimensional quantum Ising models.We begin with the transverse field Ising chain(TFIC)at quantum critical point and examine how it evolves under perturbations,such as an applied longitudinal field or weak coupling to another quantum critical TFIC.
基金supported by the National Natural Science Foundation of China(Grant No.12175316).
文摘Phase transitions,as one of the most intriguing phenomena in nature,are divided into first-order phase transitions(FOPTs)and continuous ones in current classification.While the latter shows striking phenomena of scaling and universality,the former has recently also been demonstrated to exhibit scaling and universal behavior within a mesoscopic,coarse-grained Landau-Ginzburg theory.Here we apply this theory to a microscopic model-the paradigmatic Ising model,which undergoes FOPTs between two ordered phases below its critical temperature-and unambiguously demonstrate universal scaling behavior in such FOPTs.These results open the door for extending the theory to other microscopic FOPT systems and experimentally testing them to systematically uncover their scaling and universal behavior.
基金Project supported by the Open Project of the Key Laboratory of Xinjiang Uygur Autonomous Region,China(Grant No.2021D04015)the Yili Kazakh Autonomous Prefecture Science and Technology Program Project,China(Grant No.YZ2022B021).
文摘Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.
基金V. ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China （No.21125313, No.20933006,and No.91027012）
文摘We have studied the nucleation process of a two-dimensional kinetic Ising model subject to a bias oscillating external field, focusing on how the nucleation time depends on the oscillation frequency. It is found that the nucleation time shows a clear-cut minimum with the variation of oscillation frequency, wherein the average size of the critical nuclei is the smallest, indicating that an oscillating external field with an optimal frequency can be much more favorable to the nucleation process than a constant field. We have also investigated the effect of the initial phase of the external field, which helps to illustrate the occurrence of such an interesting finding.
基金supported by the National Natural Science Foundation of China(Grant No.11304123)the Scientific Research Foundation of Jianghan University(Grant No.2010014)
文摘Many phenomena show that in a favorable circumstance an agent still has an updating possibility, and in an unfavor- able circumstance an agent also has a possibility of holding its own state and reselecting its neighbors. To describe this kind of phenomena an Ising model on evolution networks was presented and used for consensus formation and separation of opinion groups in human population. In this model the state-holding probability p and selection-rewiring probability q were introduced. The influence of this mixed dynamics of spin flips and network rewiring on the ordering behavior of the model was investigated, p hinders ordering of opinion networks and q accelerates the dynamical process of networks. Influence of q on the ordering and separating stems from its effect on average path length of networks.
基金The project supported by the Natural Science Foundation of Xiaogan University and the Science Foundation of Qufu Normal University
文摘A decorated lattice is suggested and the Ising model on it with three kinds of interactions K1, K2, and K3 is studied. Using an equivalent transformation, the square decorated Ising lattice is transformed into a regular square Ising lattice with nearest-neighbor, next-nearest-nelghbor, and four-spin interactions, and the critical fixed point is found at K1 = 0.5769, K2= -0.0671, and K3 = 0.3428, which determines the critical temperature of the system. It is also found that this system and the regular square Ising lattice, and the eight-vertex model belong to the same universality class.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50831006)
文摘An overview of the mathematical structure of the three-dimensional（3D） Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D Ising model,Reidemeister moves in the knot theory,Yang-Baxter and tetrahedron equations,the following facts are illustrated for the 3D Ising model.1） The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a（3＋1）-dimensional space-time as a relativistic quantum statistical mechanics model,which is consistent with the 4-fold integrand of the partition function obtained by taking the time average.2） A unitary transformation with a matrix that is a spin representation in 2 n·l·o-space corresponds to a rotation in 2n·l·o-space,which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model.3） A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model,and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures.4） The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases φx,φy,and φz.The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail.The conjectured exact solution is compared with numerical results,and the singularities at/near infinite temperature are inspected.The analyticity in β=1/（kBT） of both the hard-core and the Ising models has been proved only for β〉0,not for β=0.Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.
基金This work has been supported by the National Natural Science Foundation of China under grant numbers 51590883 and 51331006by the State Key Project of Research and Development of China(No.2017YFA0206302).
文摘In this work,the computational complexity of a spin-glass three-dimensional(3D)Ising model(for the lattice sizeN=lmn,wherel,m,n are thenumbersof lattice points along three crystallographic directions)is studied.We prove that an absolute minimum core(AMC)model consisting of a spin-glass 2D Ising model interacting with its nearest neighboring plane,has its computational complexity O(2mn).Any algorithms to make the model smaller(or simpler)than the AMC model will cut the basic element of the spin-glass 3D Ising model and lost many important information of the original model.Therefore,the computational complexity of the spin-glass 3D Ising model cannot be reduced to be less than O(2mn)by any algorithms,which is in subexponential time,superpolynomial.
文摘The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within the mean-field theory based on Bogoliubov inequality for the Gibbs free energy. The ground-state phase diagram and the tricritical point are obtained in the transverse field Ω/ zJ-longitudinal crystal D / zJ field plane. We find that there are the first order-order phase transitions in a very small range of D /zJ besides the usual first order-disorder phase transitions and the second order-disorder phase transitions,
文摘The review paper by Zhang Zhi-Dong （Zhang Z D 2013 Chin. Phys. B 22 030513, arXiv：1305.2956） contains many errors and is based on several earlier works that are equally wrong.
基金Project supported partially by Guangdong Natural Science Foundation (GDNSF) of China (Grant No 07300793)One of authors(Loan Mushtaq) was partially supported by the Guangdong Ministry of Education,China
文摘We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L=8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Тc=3.6403（2）. A convincing finite-size scaling analysis of the model yields ν=0.9995（21）, β/ν=0.12400（17）, γ/v=1.75223（22）, γ^1/ν=1.7555（22）, α/ν=0.00077（420） （scaling） and α/ν=0.0010（42） （hyperscaling）. The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values.
文摘An improved transverse Ising model is proposed by taking the depolarization field effect into account. Within the framework of mean-held theory we investigate the behavior of the ferroelectric thin film. Our results show that the influence of the depolarization field is to flatten the spontaneous polarization profile and make the films more homogeneous, which is consistent with Ginzburg Landau theory. This fact shows that this model can be taken as an effective model to deal with the ferroelectric film and can be further extended to refer to quantum effect. The competition between quantum effect and depolarization field induces some interesting phenomena on ferroelectric thin films.
基金Project supported by the Scientific and Technological Research Council of Turkey (TBTAK) (Grant No. 107T533)the Erciyes University Research Funds (Grant Nos. FBA-06-01 and FBD-08-593)
文摘Recently, Shiet al. [2008 Phys. Left. A 372 5922] have studied the dynamical response of the kinetic Ising model in the presence of a sinusoidal oscillating field and presented the dynamic phase diagrams by using an effective-field theory （EFT） and a mean-field theory （MFT）. The MFT results are in conflict with those of the earlier work of Tome and de Oliveira, [1990 Phys. Rev. A 41 4251]. We calculate the dynamic phase diagrams and find that our results are similar to those of the earlier work of Tome and de Oliveira; hence the dynamic phase diagrams calculated by Shiet al. are incomplete within both theories, except the low values of frequencies for the MFT calculation. We also investigate the influence of external field frequency （w） and static external field amplitude （h0） for both MFT and EFT calculations. We find that the behaviour of the system strongly depends on the values of w and h0.
文摘The effect of electron itineracy on the magnetism of S＝1/2 ferromagnetic Ising model is investigated by introducing a hopping term. The electron Green's function method is used to deal with this Hamiltonian. Here emphasis is made on that the magnetization is caused by the difference between the filling of spin-up and spin-down electrons.This concept is in accordance with that of band structure theory. In the zero band width limit, our results are the same as obtained by spin Green's function method. However, our method achieves more detailed physical information. The spontaneous magnetization, Curie temperature, total energy, and specific heat are calculated and investigated in detail by the densities of states. Hopping term depresses the Curie temperature but remains the order-disorder transformation still to be second order transition. Above the transition point, the energy band is the same as that of tight binding system because exchange interaction has no effect anymore. While under the transition point, the energy band splits into two subbands due to exchange interaction.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFE0120500)the National Natural Science Foundation of China(Grant No.51972129)+3 种基金the South Xinjiang Innovation and Development Program of Key Industries of Xinjiang Production and Construction Corps(Grant No.2020DB002)the Fundamental Research Funds for the Central Universities,China(Grant Nos.HUST 2018KFYYXJJ051 and 2019KFYXMBZ076)Shenzhen Fundamental Research Fund(Grant No.JCYJ20190813172609404)the Hubei“Chu-Tian Young Scholar”Program。
文摘The dynamic phase transition properties for ferroelectric nanotube under a spin-1/2 transverse Ising model are studied under the effective field theory(EFT)with correlations.The temperature effects on the pseudo-spin systems are unveiled in three-dimensional(3-D)and two-dimensional(2-D)phase diagrams.Moreover,the dynamic behaviors of exchange interactions on the 3-D and 2-D phase transitions under high temperature are exhibited.The results present that it is hard to obtain pure ferroelectric phase under high temperature;that is,the vibration of orderly pseudo-spins cannot be eliminated completely.
文摘The time evolution of the Hamming distance (damage spreading) for the and Ising models on the square lattice is performed with a special metropolis dynamics algorithm. Two distinct regimes are observed according to the temperature range for both models: a low-temperature one where the distance in the long-time limit is finite and seems not to depend on the initial distance and the system size; a high-temperature one where the distance vanishes in the long-time limit. Using the finite size scaling method, the dynamical phase transition (damage spreading transition) temperature is obtained as for the Ising model.
文摘We use the quantum renormalization-group（QRG） method to study the entanglement and quantum phase transition（QPT） in the one-dimensional spin-1/2 Heisenberg-Ising model [Lieb E,Schultz T and Mattis D 1961 Ann.Phys.（N.Y.） 16 407].We find the quantum phase boundary of this model by investigating the evolution of concurrence in terms of QRG iterations.We also investigate the scaling behavior of the system close to the quantum critical point,which shows that the minimum value of the first derivative of concurrence and the position of the minimum scale with an exponent of the system size.Also,the first derivative of concurrence between two blocks diverges at the quantum critical point,which is directly associated with the divergence of the correlation length.
