Slow dynamics and correlation functions

TL;DR

This paper investigates the cause of slow dynamics near phase transitions, showing that increased return probability, not transition rate slowdown, explains correlation decay in the ferromagnetic Potts model, impacting glass transition theories.

Contribution

It demonstrates that slow dynamics can result from increased return probabilities rather than transition rate reductions, challenging common assumptions.

Findings

Return probability increases near transition in the Potts model

Slow dynamics linked to return probability, not transition rates

Implications for glass transition theories

Abstract

The slow dynamics of a system as it approaches a phase transition, associated with the slowing down in the decay of a correlation function, can be caused by a sharp increase in the probability of a particle's returning to its original state following a transition, rather than to a slowing down in the transition rates as is usually assumed. The results of our calculations show that this is the case for the ferromagnetic Potts model. The implications of this result for various theories of the glass transition are discussed.