The Swendsen-Wang Process Does Not Always Mix Rapidly

The Swendsen-Wang process provides one possible dynamics for the Qstate Potts model in statistical physics. Computer simulations of this process are widely used to estimate the expectations of various observables (random variables) of a Potts system in the equilibrium (or Gibbs) distribution. The legitimacy of such simulations depends on the rate of convergence of the process to equilibrium, often known as the mixing rate. Empirical observations suggest that the Swendsen-Wang process mixes rapidly in many instances of practical interest. In spite of this, we show that there are occasions on which the Swendsen-Wang process requires exponential time (in the size of the system) to approach equilibrium. ∗ Address for correspondence: Department of Computer Science, University of Edinburgh, The King’s Buildings, Edinburgh EH9 3JZ, United Kingdom. 

• Type: Conference
• Year: 1997
• Where: STOC
• Authors: Vivek Gore, Mark Jerrum
• Keywords: Algorithms, Qstate Potts Model, STOC 1997, Swendsen-Wang Process, Swendsen-Wang Process Mixes