Study of the Two-Dimensional Anisotropic Ising Model with Competing Interactions in the Region of a Transition from the Ferromagnetic to Paramagnetic State

Abstract

The two-dimensional anisotropic Ising model with competing interactions in the region of a transition from the ferromagnetic to paramagnetic phase has been studied by the Monte Carlo method using the Wang–Landau algorithm. State density distributions have been obtained and the order parameters corresponding to different energies have been calculated. The temperature dependences of the thermodynamic parameters including the internal energy, magnetization, free energy, entropy, specific heat at constant magnetization, and Binder cumulants have been calculated. Using the Binder cumulant method and histogram analysis, it has been shown that a single second-order phase transition from the ferromagnetic to paramagnetic phase occurs at two exchange coupling constants ratios |J1/J| = 0.1 and 0.2 in the two-dimensional anisotropic next-nearest neighbor Ising model. The phase transition temperatures have been calculated. The main critical exponents have been determined using the finite-size scaling theory.