Reexamination of the long-range Potts model: a multicanonical approach

TL;DR

This paper uses a multicanonical algorithm to study the critical behavior of the one-dimensional long-range Potts model, improving recursion schemes and accurately determining transition points and the boundary between first- and second-order regimes.

Contribution

It introduces an improved multicanonical method for long-range models and precisely determines the critical threshold separating different phase transition regimes.

Findings

Transition temperatures match mean-field predictions better than previous studies.

Accurate determination of the threshold $\sigma_c(q)$ for q=3 to 9.

Numerical evidence supporting the phase transition boundary.

Abstract

We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interaction $1/r^{d+\sigma}$, using a multicanonical algorithm. The recursion scheme initially proposed by Berg is improved so as to make it suitable for a large class of LR models with unequally spaced energy levels. The choice of an efficient predictor and a reliable convergence criterion is discussed. We obtain transition temperatures in the first-order regime which are in far better agreement with mean-field predictions than in previous Monte Carlo studies. By relying on the location of spinodal points and resorting to scaling arguments, we determine the threshold value $\sigma_c(q)$ separating the first- and second-order regimes to two-digit precision within the range $3 \leq q \leq 9$. We offer convincing numerical evidence supporting $\sigma_c(q)