Fredrickson-Andersen model on Bethe lattice with random pinning

TL;DR

This paper investigates how random pinning influences the nonergodic transition in the Fredrickson-Andersen model on the Bethe lattice, revealing critical behavior and parallels with spin glass models and mode-coupling theory.

Contribution

It demonstrates the impact of random pinning on the transition temperature and critical behavior, connecting spin freezing to glass transition theories.

Findings

Transition temperature increases with pinned spins

Transition line terminates at a critical point

Correlation lengths diverge at the critical point

Abstract

We study the effects of random pinning on the Fredrickson-Andersen model on the Bethe lattice. We find that the nonergodic transition temperature rises as the fraction of the pinned spins increases and the transition line terminates at a critical point. The freezing behavior of the spins is analogous to that of a randomly pinned p-spin mean-field spin glass model which has been recently reported. The diverging behavior of correlation lengths in the vicinity of the terminal critical point is found to be identical to the prediction of the inhomogeneous mode-coupling theory at the A3 singularity point for the glass transition.