Monte Carlo simulation of two-dimensional Ising model with logarithmic exchange interaction

Amir Taheridehkordi, Roberto Zivieri

In this paper, we theoretically study the critical properties of the classical spin-1 Ising model using two approaches: 1) the analytical low-temperature series expansion and 2) the numerical Metropolis Monte Carlo technique. Within this analysis, we discuss the critical behavior of one-, two- and three-dimensional systems modeled by the first-neighbor spin-1 Ising model for different types of exchange interactions. The comparison of the results obtained according the Metropolis Monte Carlo simulations allows us to highlight the limits of the widely used mean-field theory approach. We also show, via a simple transformation, that for the special case where the bilinear and bicubic terms are set equal to zero in the Hamiltonian the partition function of the spin-1 Ising model can be reduced to that of the spin-1/2 Ising model with temperature dependent external field and temperature independent exchange interaction times an exponential factor depending on the other terms of the Hamiltonian and confirm this result numerically by using the Metropolis Monte Carlo simulation. Finally, we investigate the dependence of the critical temperature on the strength of long-range interactions included in the Ising Hamiltonian comparing it with that of the first-neighbor spin-1/2 Ising model.

Walter Selke

S. Sudhagar, N. Baskaran

We have studied the thermodynamic and magnetic properties of the spin 1/2 XXZ Ising model on a two dimensional square lattice using Monte Carlo simulation, in the presence of transverse magnetic field for varying lattice sizes (N=8-40) and exchange interaction strengths. The variations in specific heat and susceptibility for different N values is almost negligible, except for N=8. Interestingly, the magnetization showed large variation with N. This could be attributed to the increase in the disorder of spin alignment with increasing N.

Michael Faas, H. J. Hilhorst

Tota Nakamura

We develop an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with highly anisotropic exchange interactions. Both correlation time and real CPU time are reduced drastically. The algorithm is demonstrated in the layered triangular-lattice antiferromagnetic Ising model. We have obtained the relation between the transition temperature and the exchange interaction parameters, which modifies the result of the chain-mean-field theory.

XiaoWei Lei, Ji Zheng, Xiaoyu Zhao