The Growing Correlation Length in Glasses

TL;DR

This paper investigates the growth of correlation length in glasses using a single occupancy cell model, mapping it to an Ising spin glass in a field, and finds divergence near maximum packing density.

Contribution

It introduces a simplified model linking glass correlation lengths to spin glass universality classes, providing analytical and simulation insights into their behavior.

Findings

Correlation length remains finite at finite temperatures for binary liquids.

In hard disks and spheres, correlation length diverges near maximum packing density.

The divergence exponent relates to the Ising spin glass domain wall energy exponent.

Abstract

The growing correlation length observed in supercooled liquids as their temperature is lowered has been studied with the aid of a single occupancy cell model. This model becomes more accurate as the density of the system is increased. One of its advantages is that it permits a simple mapping to a spin system and the effective spin Hamiltonian is easily obtained for smooth interparticle potentials. For a binary liquid mixture the effective spin Hamiltonian is in the universality class of the Ising spin glass in a field. No phase transition at finite temperatures is therefore expected and the correlation length will stay finite right down to zero temperature. For binary mixtures of hard disks and spheres we were not able to obtain the effective spin Hamiltonian analytically, but have done simulations to obtain its form. It again is in the universality class of the Ising spin glass in a field. However, in this case the effective field can be shown to go to zero at the density of maximum packing in the model, (which is close to that of random close packing), which means that the correlation length will diverge as the density approaches its maximum. The exponent nu describing the divergence is related in d dimensions to the Ising spin glass domain wall energy exponent theta.