Finite-size effects of dimensional crossover in quasi-two-dimensional three-state Potts model

TL;DR

This study investigates how finite-size effects influence the dimensional crossover and change in the order of phase transition in a quasi-two-dimensional three-state Potts model, using Monte Carlo simulations.

Contribution

It provides the first detailed analysis of finite-size effects on the dimensional crossover in the quasi-2D three-state Potts model with Monte Carlo methods.

Findings

Finite-size scaling theory agrees with Monte Carlo results.

Dimensional crossover affects the order of the phase transition.

Finite-size effects are significant near the crossover point.

Abstract

A nearest neighbour spin pair of the quasi-two-dimensional three-state Potts model interacts with the strength $J(>0)$ in the $xy$-plane and with $\lambda J$ $(0\le \lambda \ll 1)$ in the $z$-axis. The phase transition is of second-order when $\lambda = 0$ and is of first-order when $\lambda > 0$. The dimensional crossover occurs with a change of the order of the phase transition. We study the finite-size effects of the phenomenon by using a Monte Carlo method with a multi-spin coding technique. The prediction of the finite-size scaling theory is consistent with the Monte Carlo results.