Mixing Time Power Laws at Criticality

We study the mixing time of some Markov Chains converging to critical physical models. These models are indexed by a parameter β and there exists some critical value βc where the model undergoes a phase transition. According to Physics lore, the mixing time of such Markov Chains is often of logarithmic order outside the critical regime, when β = βc, and satisfies some power law at criticality, when β = βc. We prove this in the two following settings:

• Type: Conference
• Year: 2007
• Where: FOCS
• Authors: Yun Long, Asaf Nachmias, Yuval Peres
• Keywords: Critical Physical Models, FOCS 2007, Markov Chains, Mixing Time, Theoretical Computer Science