Local, Cluster, and Transitional Monte Carlo Dynamics

Details Local, Cluster, and Transitional Monte Carlo Dynamics Local, Cluster, and Transitional Monte Carlo Dynamics

1998-07-15

arxiv.org/abs/cond-mat/9807219v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, revtex

Scientific paper

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 = sum{E'} 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' = d^2 P / d x^2 + 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.

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