Low temperature amorphous solids: mean field theory and beyond

TL;DR

This paper reviews the mean field theory of low-temperature amorphous solids in infinite dimensions, discusses their unusual features, and explores potential approaches to go beyond the mean field approximation.

Contribution

It provides a summary of the mean field theory for amorphous solids and discusses future directions to incorporate finite-dimensional effects.

Findings

Mean field theory captures key features of low-temperature amorphous solids.

The low temperature phase exhibits distinctive properties explained by the theory.

Proposes perspectives for extending beyond the mean field limit.

Abstract

Amorphous solids at low temperature display unusual features which have been escaped a clear and unified comprehension. In recent years a mean field theory of amorphous solids constructed in the limit of infinite spatial dimensions has been proposed. I will briefly review what is the outcome of this theory focusing the low temperature phase and discuss some perspectives to go beyond the mean field limit.