Constructing explicit magnetic analogies for the dynamics of glass forming liquids

TL;DR

This paper develops a magnetic analogy for glass-forming liquids by mapping their dynamics onto an Ising model with disorder, providing insights into the glass transition and replica symmetry breaking.

Contribution

It introduces a spatially varying replica overlap parameter and constructs a replica free energy functional that maps onto a disordered Ising Hamiltonian, linking liquid structure to magnetic models.

Findings

Discontinuous replica symmetry breaking may occur at low temperatures.

The model suggests a connection between configurational entropy and magnetic phase transitions.

The approach provides a new framework for understanding glassy dynamics.

Abstract

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy.