Low-temperature properties of some disordered systems from the statistical properties of nearly degenerate two-level excitations

TL;DR

This paper investigates the low-temperature thermal fluctuations in disordered systems by analyzing nearly degenerate two-level excitations in 1D models, revealing their contributions to physical observables and their universal or non-universal nature.

Contribution

It provides a detailed statistical analysis of two-level excitations in 1D disordered models and connects their properties to observable thermodynamic quantities at low temperatures.

Findings

Specific heat dominated by non-universal small excitations

Magnetic susceptibility influenced by universal large excitations

Edwards-Anderson parameter depends on disorder variance

Abstract

The thermal fluctuations that exist at very low temperature in disordered systems are often attributed to the existence of some two-level excitations. In this paper, we revisit this question via the explicit studies of the following 1D models (i) a particle in 1D random potentials (ii) the random field Ising chain with continuous disorder distribution. In both cases, we define precisely the `two-level' excitations and their statistical properties, and we show that their contributions to various observables are in full agreement at low temperature with the the rigorous results obtained independently. The statistical properties of these two-level excitations moreover yield simple identities at order $T$ in temperature for some generating functions of thermal cumulants. For the random-field Ising chain, in the regime where the Imry-Ma length is large, we obtain that the specific heat is dominated by small non-universal excitations, that depend on the details of the disorder distribution, whereas the magnetic susceptibility and the Edwards-Anderson order parameter are dominated by universal large excitations, whose statistical properties only depend on the variance of the initial disorder via the Imry-Ma length.