Critical behavior of the two-dimensional Ising model with next-nearest-neighbor antiferromagnetic interaction on the Creutz cellular automaton

Abstract

The two-dimensional Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions of ratio R is simulated on the Creutz cellular automaton. The values of the critical temperature and the critical exponents for O⩽ R < ½ are estimated within the framework of the finite size scaling theory. The dependence of T c on R agrees with the crossover scaling theory for φ = γ = 1.75. The results for 0 < R < ½ are compatible with Ising critical behavior.