Statistical mechanics of glass transition in lattice molecule models

TL;DR

This paper introduces lattice molecule models using Wang tiles to study the glass transition, revealing a thermodynamic transition to a glass phase through theoretical ground state analysis.

Contribution

It presents a novel lattice model framework with irregular ground states and identifies a thermodynamic glass transition using a new order parameter.

Findings

Existence of a thermodynamic glass transition in the model

Construction of an infinite series of irregular ground states

Identification of a glass order parameter based on ground state overlaps

Abstract

Lattice molecule models are proposed in order to study statistical mechanics of glass transition in finite dimensions. Molecules in the models are represented by hard Wang tiles and their density is controlled by a chemical potential. An infinite series of irregular ground states are constructed theoretically. By defining a glass order parameter as a collection of the overlap with each ground state, a thermodynamic transition to a glass phase is found in a stratified Wang tiles model on a cubic lattice.