engleski

Short-time dynamics of the long-range Potts model

The short-time dynamics [1] has recently attracted considerable attention by providing a ground for numerical calculation of static critical properties, which is free of critical slowing down. The concept may be extended to the long-range interactions, as it was shown for continuous n-vector and spherical models within the RG $\epsilon$-expansion [2]. We examine the applicability of dynamical Monte Carlo simulations based on this approach to discrete models with long-range interactions. We consider the one dimensional q-state Potts model with long-range power-law decaying interactions of the form $1/r^{; ; ; ; ; ; ; 1+\sigma}; ; ; ; ; ; ; $. This paradigmatic model comprises, through variation of the parameter of range $\sigma$, different critical regimes, including the onset of the first-order phase transition when $q>2$. By using different dynamical procedures, we derive the static critical exponents, and study the universal dynamical critical exponent of the initial slip, depending on $\sigma$ and number of states $q$. Particular attention is given to the tricritical point, related to the onset of the first-order regime $q_c(\sigma)$, precise location of which still escapes all the standard RG and numerical approaches [3]. \\ [1] H.K. Janssen, B. Schaub, and B. Schmittman, Z.Phys. B73, 539 (1989) [2] Y. Chen et al, Eur.Phys.J. B 18, 289 (2000) [3] E. Bayong et al., Phys.Rev.Lett. 83, 14 (1999) ; K. Uzelac, Z. Glumac, Phys.Rev.Lett. 85, 5255 (2000) ; S. Reynal, H.-T. Diep, Phys.Rev. E 69, 026109 (2004)

short-time dynamics ; long-range interactions ; Potts model ; first-order phase transition

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