2D Potts Model Correlation Lengths: Numerical Evidence for $\xi_o = \xi_d$ at $\beta_t$

TL;DR

This study uses Monte Carlo simulations to provide strong numerical evidence that the correlation lengths in the ordered and disordered phases of the 2D Potts model are equal at the first-order transition point, confirming theoretical predictions.

Contribution

The paper offers the first extensive numerical validation that the ordered and disordered correlation lengths are equal at the transition point in the 2D Potts model for q=10, 15, 20.

Findings

Correlation lengths in ordered and disordered phases are equal at $eta_t$.

Energy moments at $eta_t$ match large q-expansion predictions.

Numerical evidence supports theoretical conjectures about phase transition properties.

Abstract

We have studied spin-spin correlation functions in the ordered phase of the two-dimensional $q$-state Potts model with $q=10$, 15, and 20 at the first-order transition point $\beta_t$. Through extensive Monte Carlo simulations we obtain strong numerical evidence that the correlation length in the ordered phase agrees with the exactly known and recently numerically confirmed correlation length in the disordered phase: $\xi_o(\beta_t) = \xi_d(\beta_t)$. As a byproduct we find the energy moments in the ordered phase at $\beta_t$ in very good agreement with a recent large $q$-expansion.