Incollection,
Short-time dynamics of the long-range Potts model
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
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 to 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)
