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

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 $\sigma_c(q)<1.0$ for all $q$, by virtue of an unusual finite-size effect, namely, finite-size scaling predicts a continuous transition in the thermodynamic limit, despite the first-order nature of the transition at finite size. A qualitative account in terms of correlation lengths is provided. Finally, we find the crossover between the LR and short-range regimes to occur inside a narrow window $1.0 < \sigma < 1.2$, thus lending strong support to Sak's scenario.
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Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2004, 69, pp.026109. 〈10.1103/PhysRevE.69.026109〉
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Sylvain Reynal, Hung-The Diep. Reexamination of the long-range Potts model: a multicanonical approach. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2004, 69, pp.026109. 〈10.1103/PhysRevE.69.026109〉. 〈hal-00000424v5〉

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