Accelerated Dynamics for Monte Carlo Simulations in Statistical Mechanics.
Abstract
I discuss a new family of accelerated Monte Carlo simulation algorithms based on cluster percolation concepts. Critical slowing down hinders standard Monte Carlo simulations of statistical systems at criticality. New algorithms, featuring collective-update steps such as large cluster flips, result in increased efficiency and reduced critical slowing down. The algorithms of Swendsen-Wang and single-cluster for the Ising Model are analyzed and compared with standard algorithms. A scaling ansatz based on length rescaling arguments is introduced and shown to be in good agreement with numerical results. The dynamic critical exponents are obtained by the study of finite size scaling of autocorrelation times. Numerical results which illustrate different interesting aspects of these new dynamics are presented for the Ising Model in d = 2, 3, 4 and mean-field. An extension of the Swendsen -Wang dynamics to continuous spin models such as the Landau -Ginzburg (phi^4 scalar field theory) is introduced. This model based on an "embedding" scheme is shown to reduce critical slowing down and conjectured to lie in the same dynamic universality class as the Swendsen -Wang Ising model. Finally the effect of global vs local conservation laws in critical dynamics is studied by two techniques: global exchange and magnetization-demon exchange. Global conservation seems to be enough to characterize Hohenberg and Halperin's Model B dynamical universality class.
- Publication:
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Ph.D. Thesis
- Pub Date:
- 1991
- Bibcode:
- 1991PhDT........53T
- Keywords:
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- Physics: Condensed Matter; Physics: General; Statistics