Phase Transition and Surface Sublimation of a Mobile Potts Model

TL;DR

This paper investigates phase transitions and surface sublimation in a mobile Potts model using Monte Carlo simulations and mean-field approximations, revealing temperature-dependent surface and bulk behaviors.

Contribution

It introduces a combined Monte Carlo and mean-field approach to study surface sublimation and phase transitions in a mobile Potts model with variable concentration.

Findings

Surface spins detach at high temperature, forming a gas.

Interior spins undergo a first-order phase transition at high concentration.

Mean-field results confirm the first-order nature of the transition.

Abstract

We study in this paper the phase transition in a mobile Potts model by the use of Monte Carlo simulation. The mobile Potts model is related to a diluted Potts model which is also studied here by a mean-field approximation. We consider a lattice where each site is either vacant or occupied by a $q$-state Potts spin. The Potts spin can move from one site to a nearby vacant site. In order to study the surface sublimation, we consider a system of Potts spins contained in a recipient with a concentration $c$ defined as the ratio of the number of Potts spins $N_s$ to the total number of lattice sites $N_L = N_x \times N_y \times N_z$. Taking into account the attractive interaction between the nearest-neighboring Potts spins, we study the phase transition as functions of various physical parameters such as the temperature, the shape of the recipient and the spin concentration. We show that as the temperature increases, surface spins are detached from the solid phase to form a gas in the empty space. Surface order parameters indicate different behaviors depending on the distance to the surface. At high temperatures, if the concentration is high enough, the interior spins undergo a first-order phase transition to an orientationally disordered phase. The mean-field results are shown as functions of temperature, pressure and chemical potential, which confirm in particular the first-order character of the transition.