The long-ranged Potts model revisited: a multicanonical approach
Résumé
We investigate the critical behavior of the one-dimensional q-state Potts model with long-ranged (LR) interaction $1/r^{d+\sigma}$, using a multicanonical algorithm.The recursion scheme initially proposed by Berg is improved so as to makeit suitable for a large class of LR models with unequally spaced out 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 agreementwith mean-field predictions than in any previous study.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 regime to an unprecedented two digit precision within the range $3 \leq q \leq 9$.We offer convincing numerical evidence supporting $\sigma_c(q)<1.0$ for all $q$, by virtue ofan unusual finite-size effect which has not been noticed before, namely finite-size scaling predicts a second-order transition in the thermodynamic limit, despite the first-order nature of transitions at finite size. A qualitative account in terms of correlation lengths is provided.Finally, we find the cross-over between LR and short-range regimes to occur inside a narrow window $1.0 < \sigma < 1.2$, thus lending strong support to Sak's scenario.