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

We investigate the critical behavior of the one-dimensional q-state Potts model with long-range (LR) interaction $1\mathrm{/}{r}^{d+\sigma }$, 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 $3\le q\le 9$. We offer convincing numerical evidence supporting $\sigma_c(q)