A 1ST-ORDER PHASE-TRANSITION IN THE 3-DIMENSIONAL 4-STATE ANTIFERROMAGNETIC POTTS-MODEL

We study the four-state antiferromagnetic Potts model with next-nearest-neighbour ferromagnetic interactions on the simple cubic lattice by the Monte Carlo method. The ratio J2/J1 of the strength of the next-nearest-neighbour interactions to that of the nearest-neighbour interactions is to be 10. We analyse the finite-size effects of the energy, the specific heat, the fourth-order cumulant, the magnetization, the susceptibility and the effective transition temperatures. With the help of the finite-size scaling theory we conclude that the transition of the model is assigned to be of first order.