Thermodynamic, critical properties and phase transitions of the Ising model on a square lattice with competing interactions

The thermodynamic and critical properties, and phase transitions of two-dimensional Ising model on a square lattice with competing interactions are investigated by the Monte Carlo method. Estimations are made for the magnitude relations of the next-nearest-neighbor and nearest-neighbor exchange interactions r=J(2)/J(1) in the value ranges of 0.1 <= r <= 1.0. The anomalies of thermodynamic observables are shown to be present in this model on the interval 0.45 <= r <= 0.5. The phase diagram for the dependence of the critical temperature on a value of next-nearest neighbor interaction is plotted. A phase transition for all values in the interval 0.45 <= r <= 0.5 is shown to be a second order. Our data show that the temperature of the heat capacity maximum at r=0.5 tends to a finite value. The static critical exponents of the heat capacity a, susceptibility gamma, order parameter beta, correlation length nu, and the Fisher exponent eta are calculated by means of the finite-size scaling theory. It is found that the change in next-nearest neighbor interaction value in the range 0.7 <= r <= 1.0 leads to nonuniversal critical behavior. (C) 2016 Elsevier Ltd. All rights reserved.