Finitely coordinated models for low-temperature phases of amorphous systems

Abstract

We introduce models of heterogeneous systems with finite connectivity defined\non random graphs to capture finite-coordination effects on the low-temperature\nbehavior of finite dimensional systems. Our models use a description in terms\nof small deviations of particle coordinates from a set of reference positions,\nparticularly appropriate for the description of low-temperature phenomena. A\nBorn-von-Karman type expansion with random coefficients is used to model\neffects of frozen heterogeneities. The key quantity appearing in the\ntheoretical description is a full distribution of effective single-site\npotentials which needs to be determined self-consistently. If microscopic\ninteractions are harmonic, the effective single-site potentials turn out to be\nharmonic as well, and the distribution of these single-site potentials is\nequivalent to a distribution of localization lengths used earlier in the\ndescription of chemical gels. For structural glasses characterized by\nfrustration and anharmonicities in the microscopic interactions, the\ndistribution of single-site potentials involves anharmonicities of all orders,\nand both single-well and double well potentials are observed, the latter with a\nbroad spectrum of barrier heights. The appearance of glassy phases at low\ntemperatures is marked by the appearance of asymmetries in the distribution of\nsingle-site potentials, as previously observed for fully connected systems.\nDouble-well potentials with a broad spectrum of barrier heights and asymmetries\nwould give rise to the well known universal glassy low temperature anomalies\nwhen quantum effects are taken into account.\n