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

Abstract

Abstract 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 α , susceptibility γ , order parameter β , correlation length ν , and the Fisher exponent η 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.