1998/07/15 by Jian‐Sheng Wang, Jian-Sheng Wang, Wang, Jian-Sheng
Physics and Astronomy · #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/9807219
8 pages, revtex
arxiv created 1998/07/15 · arxiv updated 2009/11/30
We review the local Monte Carlo dynamics and Swendsen-Wang cluster algorithm. We introduce and analyze a new Monte Carlo dynamics known as transitional Monte Carlo. The transitional Monte Carlo algorithm samples energy probability distribution P(E) with a transition matrix obtained from single-spin-flip dynamics. We analyze the relaxation dynamics master equation, d P(E, t)/ dt = sumE' T(E,E') P(E',t), associated with Ising model in d dimensions. In one dimension, we obtain an exact solution. We show in all dimensions in the continuum limit the dynamics is governed by the partial differential equation d P/dt' = d2 P / d x2 + x dP/dx + P. where x and t' are rescaled energy deviation from the equilibrium value and rescaled time, respectively. This equation is readily solved. Thus, we have a complete understanding of the dynamics.