Multilattice microcanonical simulation of the three-dimensional three-state Potts model

Abstract

The three-state Potts model with nearest-neighbor ferromagnetic interactions on a three-dimensional simple cubic lattice is studied numerically by the multilattice microcanonical simulation. This simulation allows for the determination of the van der Waals curve of metastable and unstable states in the energy-temperature curve, which demonstrates that the transition is first order and allows for the determination of the transition temperature via a Maxwell equal-area construction. We have obtained the temperature dependence of the energy, constant-volume heat capacity, and order parameter, as well as the order-parameter correlation function at selected temperatures above and below the phase transition point. Our main results for a lattice of N${=16}^{3}$ spins are the first-order transition temperature ${k}_{B}$${T}^{\mathrm{*}}$/J=1.81618(7), latent heat per spin L/JN=0.2222(7), entropy jump per spin \ensuremath{\Delta}S/${k}_{B}$N=0.122(3), constant-volume specific-heat discontinuity per spin \ensuremath{\Delta}${C}_{V}$/${k}_{B}$N=9.0(5), and order-parameter discontinuity \ensuremath{\Delta}M=0.460(5). We also present results for a lattice of N${=32}^{3}$ to examine finite-size effects.