Glass and polycrystal states in a lattice spin model

TL;DR

This study uses a lattice spin model to simulate supercooled liquids and glasses, revealing how metastability, nucleation, and off-equilibrium dynamics relate to glass and crystal formation, with implications for understanding Kauzmann's paradox.

Contribution

It introduces a lattice spin model that captures supercooled liquid and glass behaviors, including metastability, nucleation, and off-equilibrium dynamics, providing insights into the glass transition and Kauzmann's paradox.

Findings

Supercooled liquids exhibit fragile dynamics with stretched exponential relaxation.

Below the spinodal temperature, liquids become unstable and nucleate crystals.

Early off-equilibrium dynamics mimic glasses, with FDT violations and slow crystal growth.

Abstract

We numerically study a nondisordered lattice spin system with a first order liquid-crystal transition, as a model for supercooled liquids and glasses. Below the melting temperature the system can be kept in the metastable liquid phase, and it displays a dynamic phenomenology analogous to fragile supercooled liquids, with stretched exponential relaxation, power law increase of the relaxation time and high fragility index. At an effective spinodal temperature Tsp the relaxation time exceeds the crystal nucleation time, and the supercooled liquid loses stability. Below Tsp liquid properties cannot be extrapolated, in line with Kauzmann's scenario of a `lower metastability limit' of supercooled liquids as a solution of Kauzmann's paradox. The off-equilibrium dynamics below Tsp corresponds to fast nucleation of small, but stable, crystal droplets, followed by extremely slow growth, due to the presence of pinning energy barriers. In the early time region, which is longer the lower the temperature, this crystal-growth phase is indistinguishable from an off-equilibrium glass, both from a structural and a dynamical point of view: crystal growth has not advanced enough to be structurally detectable, and a violation of the fluctuation-dissipation theorem (FDT) typical of structural glasses is observed. On the other hand, for longer times crystallization reaches a threshold beyond which crystal domains are easily identified, and FDT violation becomes compatible with ordinary domain growth.