Finitely coordinated models for low-temperature phases of amorphous systems

TL;DR

This paper introduces models for low-temperature amorphous systems with finite connectivity, capturing heterogeneity effects and revealing the emergence of glassy phases with diverse potential landscapes.

Contribution

It develops a self-consistent framework for effective single-site potentials in heterogeneous, low-temperature amorphous models, including anharmonic and double-well potentials.

Findings

Harmonic interactions lead to harmonic effective potentials.

Structural glasses exhibit anharmonic and double-well potentials.

Glassy phases show asymmetries in potential distributions.

Abstract

We introduce models of heterogeneous systems with finite connectivity defined on random graphs to capture finite-coordination effects on the low-temperature behavior of finite dimensional systems. Our models use a description in terms of small deviations of particle coordinates from a set of reference positions, particularly appropriate for the description of low-temperature phenomena. A Born-von-Karman type expansion with random coefficients is used to model effects of frozen heterogeneities. The key quantity appearing in the theoretical description is a full distribution of effective single-site potentials which needs to be determined self-consistently. If microscopic interactions are harmonic, the effective single-site potentials turn out to be harmonic as well, and the distribution of these single-site potentials is equivalent to a distribution of localization lengths used earlier in the description of chemical gels. For structural glasses characterized by frustration and anharmonicities in the microscopic interactions, the distribution of single-site potentials involves anharmonicities of all orders, and both single-well and double well potentials are observed, the latter with a broad spectrum of barrier heights. The appearance of glassy phases at low temperatures is marked by the appearance of asymmetries in the distribution of single-site potentials, as previously observed for fully connected systems. Double-well potentials with a broad spectrum of barrier heights and asymmetries would give rise to the well known universal glassy low temperature anomalies when quantum effects are taken into account.