Ordered vs Disordered: Correlation Lengths of 2D Potts Models at \beta_t

TL;DR

This study uses Monte Carlo simulations to compare correlation lengths in ordered and disordered phases of 2D Potts models at first-order transition points, finding they are approximately equal.

Contribution

It provides numerical evidence that the correlation lengths in ordered and disordered phases are equal at the transition point for high-q Potts models.

Findings

Correlation length in disordered phase matches analytic predictions.

Correlation lengths in ordered and disordered phases are approximately equal.

Results support the hypothesis of equal correlation lengths at transition.

Abstract

We performed Monte Carlo simulations of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ and measured the spin-spin correlation function at the first-order transition point $\beta_t$ in the disordered and ordered phase. Our results for the correlation length $\xi_d(\beta_t)$ in the disordered phase are compatible with an analytic formula. Estimates of the correlation length $\xi_o(\beta_t)$ in the ordered phase yield strong numerical evidence that $R \equiv \xi_o(\beta_t)/\xi_d(\beta_t) = 1$.