Monte Carlo simulation of the antiferromagnetic four-state Potts model on simple cubic and body-centered-cubic lattices

Abstract

The phase transition of four-state antiferromagnetic Potts model on simple cubic and body-centered-cubic lattice is studied by cluster Monte Carlo simulations of finite systems up to ${96}^{3}$ lattice sizes. The result indicates that the size ${96}^{3}$ is still sufficient to extract asymptotic behavior. However, if one assumes that both models are well described by the usual Ginzburg-Landau Hamiltonian, the result is consistent with the prediction of the field-theoretical analysis that the phase transition is first-order one.