Critical exponents of the two-layer Ising model

Abstract

The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalisation group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction 1.75 with 1.3% deviation.

The Phase Diagrams of Spin-1/2 Ising Model on a Two-Layer Bethe Lattice with AFM/AFM Interactions

“…Let us note also that in order to use as a guide in calculating the temperature dependent PDs, first we obtain the GS PDs on the (J 2 /|J 1 …”

“…The symmetric two-layer Ising model was studied by the corner transfer matrix renormalization group method to calculate the critical points and critical exponents [1]. The Monte Carlo (MC) simulation was used to study the behavior of an Ising model consisting of two FM layers with different interaction constants coupled weakly together [2].…”

Cellular Automata Simulation of Two-Layer Ising and Potts Models

“…In recent years, some approximation methods have been applied to this model (Angelini et al, 1995;Horiguchi et al, 1996;Angelini et al, 1997 andLipowski &Suzuki, 1998). It is also argued that the two-layer Ising model is in the same universality class as the two dimensional Ising model (Li et al, 2001). Since the exact solution of the Ising model exists only for the one-and two-dimensional models, the simulation and numerical methods may be used to obtain the critical data for other models.…”

“…Then, the obtained results have been fitted in order to obtain a general ansatz equation for the critical point for the anisotropic two-layer Potts model in terms of inter-and intralayer couplings (ξ and ) as follow, (Ghaemi et al, 2003). b From the corner transfer matrix renormalization group method (Li et al, 2001) (Mardani et al, 2005) Table 2. The critical points for the 3-states two-layer Potts model There are some features which can be mentioned here with the physical aspects according to eqs.22-23.…”

The mixed spin-1/2 and spin-1 Ising system on a two-layer Bethe lattice

“…The symmetric two-layer Ising model was studied by the corner transfer matrix renormalization group method for critical points and exponents [43] calculations. Monte Carlo simulations were also performed to investigate the Ising model consisting of two FM layers coupled weakly together [44] with different interaction constants.…”