Monte Carlo algorithms based on the number of potential moves

✍ Scribed by Jian-Sheng Wang; Lik Wee Lee

• Book ID: 104110733
• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 112 KB
• Volume: 127
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/s0010-4655(00)00016-3

✦ Synopsis

We discuss Monte Carlo dynamics based on N(σ, E) E , the (microcanonical) average number of potential moves which increase the energy by E in a single spin flip. The microcanonical average can be sampled using Monte Carlo dynamics of a single spin flip with a transition rate min(1, N(σ , E -E ) E / N(σ, E -E) E ) from energy E to E . A cumulative average (over Monte Carlo steps) can be used as a first approximation to the exact microcanonical average in the flip rate. The associated histogram is a constant independent of the energy. The canonical distribution of energy can be obtained from the transition matrix Monte Carlo dynamics. This second dynamics has fast relaxation time -at the critical temperature the relaxation time is proportional to specific heat. The dynamics are useful in connection with reweighting methods for computing thermodynamic quantities.