Phase Transitions in Ising Square Antiferromagnets: A Controversial System

Abstract

The phase transitions occurring in the Ising square antiferromagnet with first- (J ₁) and second- (J ₂) nearest-neighbors interactions are studied as a function of the V(≡ J ₂/J ₁) parameter using the Monte Carlo simulation method. Our simulation results based on the analysis of the magnetization at the critical temperature indicate that the system undergoes a second-order phase transition for V < 0.5 and a first-order phase transition for 0.5 < V < 1.35. Our results confirm previous calculations performed within the 9-point approximation of the cluster variation method.