Lattice models of disorder with order

TL;DR

This paper explores lattice models with crystalline ground states to understand disorder in systems like glasses, focusing on how simple models evolve into glassy states after low-temperature quenches.

Contribution

It introduces and analyzes simple lattice models, including Potts and exclusion models, to study the transition from crystalline to glassy states in disordered systems.

Findings

Potts and exclusion models evolve into glassy states after low-temperature quenches.

Models have finite connectivity and are not constrained by evolution rules.

Crystalline ground states serve as a basis for studying disorder.

Abstract

This paper describes the use of simple lattice models for studying the properties of structurally disordered systems like glasses and granulates. The models considered have crystalline states as ground states, finite connectivity, and are not subject to constrained evolution rules. After a short review of some of these models, the paper discusses how two particularly simple kinds of models, the Potts model and the exclusion models, evolve after a quench at low temperature to glassy states rather than to crystalline states.