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

The two-dimensional Ising model with nearest-neighbor, next-nearest-neighbor and four-spin interactions is simulated on the Creutz cellular automaton. For J'less than or equal to 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'less than or equal to 0 are in a good agreement with their theoretical values of alpha=0, beta=1/8, gamma=7/4, eta=1/4 and nu=1 for the Ising model.