The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions

TL;DR

This paper studies the dynamics of a spin model with random pinning on Bethe lattices, revealing phase transitions and critical behavior similar to Mode Coupling Theory, including logarithmic relaxation and diverging times.

Contribution

It introduces a detailed analysis of the Fredrickson-Andersen model with random pinning, connecting glassy dynamics to Random Field Ising Model universality classes.

Findings

Identification of a line of dynamical transitions with Mode Coupling Theory universality

Observation of logarithmic relaxation at the terminal point

Divergence of relaxation time exponentially at criticality

Abstract

We investigate the dynamics of the randomly pinned Fredrickson-Andersen model on the Bethe lattice. We find a line of random pinning dynamical transitions whose dynamical critical properties are in the same universality class of the $A_2$ and $A_3$ transitions of Mode Coupling Theory. The $A_3$ behavior appears at the terminal point, where the relaxation becomes logarithmic and the relaxation time diverges exponentially. We explain the critical behavior in terms of self-induced disorder and avalanches, strengthening the relationship discussed in recent works between glassy dynamics and Random Field Ising Model.