Low Temperature Specific Heat of some Quantum Mean Field glassy phases

TL;DR

This paper analytically studies the low-temperature specific heat behavior in various quantum disordered models, revealing a universal $T^3$ dependence due to a common marginality mechanism within the Mean Field approximation.

Contribution

It demonstrates a universal $T^3$ specific heat behavior across different quantum disordered models, linked to the marginality condition, within the Mean Field framework.

Findings

All models exhibit $C_v(T) o T^3$ at low temperatures.

The marginality condition causes cancellation of linear and quadratic terms.

The result applies to vibrational modes, p-spin-glass, and Heisenberg spin glass.

Abstract

We investigate analytically the low temperature behavior of the specific heat $C_v(T)$ for a large class of quantum disordered models within Mean Field approximation. This includes the vibrational modes of a lattice pinned by impurity disorder in the quantum regime, the quantum spherical $p$-spin-glass and a quantum Heisenberg spin glass. We exhibit a general mechanism, common to all these models, arising from the so-called marginality condition, responsible for the cancellation of the linear and quadratic contributions in $T$ in the specific heat. We thus find for all these models the Mean Field result $C_v(T) \propto T^3$.