Finite size scaling and first order phase transition in a modified XY-model

TL;DR

This study uses Monte Carlo simulations with cluster algorithms to analyze a modified 2D XY-model, revealing first-order phase transition characteristics and unique correlation function behaviors.

Contribution

It demonstrates the first-order scaling behavior in a modified XY-model using advanced simulation techniques and multiple histogram reweighting.

Findings

First-order scaling behavior confirmed for specific heat and susceptibility

Correlation functions decay differently above the transition

Non-zero plateau observed in higher order correlation functions

Abstract

Monte Carlo simulation has been performed in a two-dimensional modified XY-model first proposed by Domany et. al [E. Domany, M. Schick and R. H. Swendsen, Phys. Rev. Lett. 52, 1535 (1984)]. The cluster algorithm of Wolff has been used and multiple histogram reweighting is performed. The first order scaling behavior of the quantities like specific heat, order parameter susceptibility and free energy barrier are found to be obeyed accurately. While the lowest order correlation function was found to decay to zero at long distance just above the transition, the next higher order correlation function shows a non-zero plateau.