Critical properties of the two-dimensional Ising model on a square lattice with competing interactions

Abstract

The critical properties of two-dimensional (2D) square lattice Ising model with next-nearest-neighbor interactions are investigated by the replica Monte Carlo method. Estimations are made for the magnitude relations of the next-nearest-neighbor and nearest-neighbor exchange interactions r=J2/J1 in the value ranges r∈[0.0,0.4] and r∈[0.7,1.0] with Δr=0.1. The static critical exponents of the heat capacity, the susceptibility, the ordering parameter, and the correlation length, as well as the Fisher exponent, are calculated by means of the finite-size scaling theory. The universality class of the critical behavior of this model is revealed to remain within the limits of values r∈ [0.0,0.4]. It is found that the change in the next-nearest-neighbor interaction value in the range r∈[0.7,1.0] leads to nonuniversal critical behavior.