Correlation Function at ${\beta }_t$ in the Disordered Phase of 2D Potts Models

We use Monte Carlo simulations to measure the spin-spin correlation function in the disordered phase of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ at the first-order transition point ${\beta }_t$. To extract the correlation length ${\xi }_d$ from the exponential decay of the correlation function over several decades with the desired accuracy we make extensively use of cluster-update techniques and improved estimators. Our results for ${\xi }_d$ are compatible with an analytic formula. As a byproduct we also measure the energy moments in the disordered phase and find very good agreement with a recent large $q$ expansion at ${\beta }_t$.