Scaling laws for the 2d 8-state Potts model with Fixed Boundary Conditions

TL;DR

This paper investigates the scaling laws and finite-size effects of the 2D 8-state Potts model with fixed boundaries through Monte Carlo simulations, revealing deviations from periodic boundary results.

Contribution

It provides empirical validation of new scaling laws for first order phase transitions with fixed boundaries in the 2D Potts model.

Findings

Supports a pseudo-critical beta finite-size scaling of beta(infinity)+a/L+b/L^2

Finds a latent heat value of 0.294(11) for fixed boundaries

Shows discrepancy with latent heat under periodic boundary conditions

Abstract

We study the effects of frozen boundaries in a Monte Carlo simulation near a first order phase transition. Recent theoretical analysis of the dynamics of first order phase transitions has enabled to state the scaling laws governing the critical regime of the transition. We check these new scaling laws performing a Monte Carlo simulation of the 2d, 8-state spin Potts model. In particular, our results support a pseudo-critical beta finite-size scaling of the form beta(infinity) + a/L + b/L^2, instead of beta(infinity) + c/L^d + d/L^{2d}. Moreover, our value for the latent heat is 0.294(11), which does not coincide with the latent heat analytically derived for the same model if periodic boundary conditions are assumed, which is 0.486358...