Transport properties and phase diagram of the disordered lattice vibration model

TL;DR

This paper investigates the transport and localization behaviors of scalar vibrations in a disordered lattice model, revealing a complex phase diagram with multiple phases affecting heat conduction and vibrational localization.

Contribution

It introduces a detailed phase diagram for a disordered lattice vibration model, identifying novel phases with anomalous localization and transport properties.

Findings

Discovery of a phase with anomalous, sub-exponential localization.

Identification of a strongly conducting phase with diverging diffusivity.

Observation of anomalous heat conductivity increasing with system size.

Abstract

We study the transport and localization properties of scalar vibrations on a lattice with random bond strength by means of the transfer matrix method. This model has been recently suggested as a means to investigate the vibrations and heat conduction properties of structural glasses. In three dimensions we find a very rich phase diagram. The delocalization transition is split, so that between the localized and diffusive phases which have been identified in the Anderson problem, we observe a phase with anomalous, sub-exponential localization. For low frequencies, we find a strongly conducting phase with ballistic and super-diffusive transport, reflecting a diverging diffusivity. The last phase generates an anomalous heat conductivity which grows with the system size. These phases are the counterparts of those identified in an earlier study of the normal modes.