Abstract
Using the finite cluster approximation (FCA) based on a single-site cluster theory and Monte Carlo simulation (MCS) under the Metropolis algorithm, we study the critical properties of two-dimensional (2D) spins-½ system by analyzing the effect of the anisotropic parameter [Formula: see text] and next-nearest-neighbor (NNN) interaction [Formula: see text] on the critical temperature [Formula: see text] of the 2D anisotropic square lattice. It is found that the MCS is more reliable than the FCA method in the resolution of the Ising model. Moreover, MC calculations reveal that [Formula: see text] is strongly correlated with the external magnetic field [Formula: see text], [Formula: see text], and [Formula: see text], where the competition between these parameters can generate several rich phase diagrams.
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