Critical configurations and tube of typical trajectories for the Potts and Ising models with zero external field

Abstract

We consider the ferromagnetic q-state Potts model with zero external field in a finite volume evolving according to Glauber-type dynamics described by the Metropolis algorithm in the low temperature asymptotic limit. Our analysis concerns the multi-spin system that has q stable equilibria. Focusing on grid graphs with periodic boundary conditions, we study the tunneling between two stable states and from one stable state to the set of all other stable states. In both cases we identify the set of gates for the transition and prove that this set has to be crossed with high probability during the transition. Moreover, we identify the tube of typical paths and prove that the probability to deviate from it during the transition is exponentially small.

44 pages, 15 figures. All comments are welcome!

References in corpus (3)

• Relaxation Height in Energy Landscapes: an Application to Multiple Metastable States
• Metastability for the degenerate Potts Model with negative external magnetic field under Glauber dynamics
• Effect of energy degeneracy on the transition time for a series of metastable states: application to Probabilistic Cellular Automata

Cited by in corpus (3)

• Metastability for the degenerate Potts Model with negative external magnetic field under Glauber dynamics
• Critical Droplets and sharp asymptotics for Kawasaki dynamics with weakly anisotropic interactions. Extended version
• Metastability of Ising and Potts models without external fields in large volumes at low temperatures