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=J2/J1 in the value ranges of 0.1≤r≤1.0.•The anomalies of thermodynamic parameters 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.

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=J2/J1 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.