PHASE-TRANSITIONS IN ISING SQUARE ANTIFERROMAGNETS WITH 1ST-NEIGHBOR AND 2ND-NEIGHBOR INTERACTIONS

The phase transitions occurring in the Ising square antiferromagnet with first- (J1) and second- (J2) nearest-neighbour interactions are studied using several mean-field approximations and for a wide range of R = J2/J1. The largest approximation used corresponds to a nine-point cluster approximation of the cluster variation method. In this case, the transition temperatures as a function of R are found to be in excellent agreement with those obtained by other methods. The mean-field approximations predict a first-order transition in the range 0.5 < R less-than-or-similar-to 1.2, where the critical exponents associated with the paramagnetic to superantiferromagnetic transition have been reported to vary continously with R. In that range of R, the mean-field approximations also predict a crossover between two distinct instability temperatures, or spinodals, taking place immediately below the first-order transition. Mean-field results are also given for the magnetization m, the specific heat C(v), the magnetic susceptibility chi, the staggered susceptibility chi(s), and the pair correlation function sigma(ij) between i and j sites.