Mixing times for the Swapping Algorithm on the Blume-Emery-Griffiths Model

Abstract

We analyze the so called Swapping Algorithm, a parallel version of the well-known Metropolis-Hastings algorithm, on the mean-field version of the Blume-Emery-Griffiths model in statistical mechanics. This model has two parameters and depending on their choice, the model exhibits either a first, or a second order phase transition. In agreement with a conjecture by Bhatnagar and Randall we find that the Swapping Algorithm mixes rapidly in presence of a second order phase transition, while becoming slow when the phase transition is first order.

arXiv comment35 pages, to be published in Random Structures and Algorithms

References in corpus (4)

• Simulated Tempering: A New Monte Carlo Scheme
• Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions
• Asymptotic behavior of the finite-size magnetization as a function of the speed of approach to criticality
• Ginzburg-Landau Polynomials and the Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points