The thermodynamics and the phase diagram of random field Ising model （RFIM） on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field （B）. A Gaussian distribution ...The thermodynamics and the phase diagram of random field Ising model （RFIM） on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field （B）. A Gaussian distribution of random field （hi） with zero mean and variance （hi2 = H2RF is considered. The free-energy （F）, the magnetization （M） and the order parameter （q） are investigated for several values of coordination number （z）. The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature Tc = J/k and when HRF = 0 for finite z. The free-energy （F） values increase as T increases for different intensities of random field （HRE） and finite z. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases, The ferromagnetic （FM） paramagnetic （PM） phase boundary is clearly observed only when z →∞. While FM PM-spin glass （SG） phase boundaries are present for finite z. The magnetic susceptibility （X） shows a sharp cusp at Tc in a small random field for finite z and rounded different peaks on increasing HRF.展开更多
文摘The thermodynamics and the phase diagram of random field Ising model （RFIM） on Bethe lattice are studied by using a replica trick. This lattice is placed in an external magnetic field （B）. A Gaussian distribution of random field （hi） with zero mean and variance （hi2 = H2RF is considered. The free-energy （F）, the magnetization （M） and the order parameter （q） are investigated for several values of coordination number （z）. The phase diagram shows several interesting behaviours and presents tricritical point at critical temperature Tc = J/k and when HRF = 0 for finite z. The free-energy （F） values increase as T increases for different intensities of random field （HRE） and finite z. The internal energy （U） has a similar behaviour to that obtained from the Monte Carlo simulations. The ground state of magnetization decreases as the intensity of random field HRF increases, The ferromagnetic （FM） paramagnetic （PM） phase boundary is clearly observed only when z →∞. While FM PM-spin glass （SG） phase boundaries are present for finite z. The magnetic susceptibility （X） shows a sharp cusp at Tc in a small random field for finite z and rounded different peaks on increasing HRF.
