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
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
We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies JA-...We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies JA-A and JA--B in this lattice. Our study is focused on how the ratio of JA-B to JA--A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, etc each as a function of temperature for a given ratio of JA-B to JA-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio JA-B / JA--A. This work is helpful for studying the phase transition problem of crystals composed of compounds.展开更多
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.
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 No 10571091)the National Science and Technology Supporting Program of China(Grant No 2006BAD11A07)
文摘We use the Monte Carlo method to study an antiferromagnetical Ising spin system on a centred honeycomb lattice, which is composed of two kinds of 1/2 spin particles A and B. There exist two different bond energies JA-A and JA--B in this lattice. Our study is focused on how the ratio of JA-B to JA--A influences the critical behaviour of this system by analysing the physical quantities, such as the energy, the order parameter, the specific heat, susceptibility, etc each as a function of temperature for a given ratio of JA-B to JA-A. Using these results together with the finite-size scaling method, we obtain a phase diagram for the ratio JA-B / JA--A. This work is helpful for studying the phase transition problem of crystals composed of compounds.
