Critical exponents of the two-dimensional Ising model with next-nearest-neighbor and four-spin interactions on the Creutz cellular automaton

Abstract

The two-dimensional Ising model with nearest-neighbor, next-nearest-neighbor and four-spin interactions is simulated on the Creutz cellular automaton. For J′⩽0 the values of critical exponents in the antiferromagnetic interaction region are estimated within the framework of the finite-size scaling theory. The calculated exponents for interaction ratios R= 1 20 and J′⩽0 are in a good agreement with their theoretical values of α=0, β= 1 8 , γ = 7 4 , η= 1 4 and v=1 for the Ising model.