Trap dominated dynamics of classical dimer models

TL;DR

This paper investigates the dynamics of classical dimer models near phase transitions, revealing trap-dominated relaxation behaviors that depend on the transition type, including exponential and Vogel-Fulcher divergence.

Contribution

It introduces a trap-based framework to understand the critical dynamics of classical dimer models, highlighting entropic traps and their impact on relaxation.

Findings

Relaxation can be exponential or sub-exponential depending on the transition.

Relaxation times diverge exponentially following Vogel-Fulcher law near criticality.

Locally jammed states create entropic traps that dominate dynamics.

Abstract

We consider dynamics of classical dimer models undergoing a phase transition to an ordered, frozen state. Relaxation processes are dominated by traps which are entropic in origin and can be traced to the locally jammed nature of the dimer states. Depending on the nature of the phase transition, critical dynamics are characterized either by an exponential, or sub-exponential in time relaxation of the order parameter. In the latter case relaxation time scales diverge {\em exponentially} as the critical point is approached, following the Vogel-Fulcher law.