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

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 $β_t$ in the disordered and ordered phase. Our results for the correlation length $ξ_d(β_t)$ in the disordered phase are compatible with an analytic formula. Estimates of the correlation length $ξ_o(β_t)$ in the ordered phase yield strong numerical evidence that $R \equiv ξ_o(β_t)/ξ_d(β_t) = 1$.