Exact Persistence Exponent for One-dimensional Potts Models with Parallel Dynamics
统计力学
2009-11-07 v1
摘要
We obtain \theta_p(q) = 2\theta_s(q) for one-dimensional q-state ferromagnetic Potts models evolving under parallel dynamics at zero temperature from an initially disordered state, where \theta_p(q) is the persistence exponent for parallel dynamics and \theta_s(q) = -{1/8}+ \frac{2}{\pi^2}[cos^{-1}{(2-q)/q\sqrt{2}}]^2 [PRL, {\bf 75}, 751, (1995)], the persistence exponent under serial dynamics. This result is a consequence of an exact, albeit non-trivial, mapping of the evolution of configurations of Potts spins under parallel dynamics to the dynamics of two decoupled reaction diffusion systems.
引用
@article{arxiv.cond-mat/0111013,
title = {Exact Persistence Exponent for One-dimensional Potts Models with Parallel Dynamics},
author = {Gautam I. Menon and P. Ray},
journal= {arXiv preprint arXiv:cond-mat/0111013},
year = {2009}
}
备注
13 pages Latex file, 5 postscript figures