Step-wise responses in mesoscopic glassy systems: a mean field approach

TL;DR

This paper investigates the step-wise responses of mesoscopic glassy systems using mean-field spin-glass models with 1-step replica symmetry breaking, revealing how finite-size effects and thermodynamic limits influence response behaviors and static chaos.

Contribution

It introduces a detailed analysis of step-wise responses in mesoscopic glassy systems through a mean-field approach, highlighting the transition to smooth responses in the thermodynamic limit.

Findings

Finite-sized systems show distinct step-wise responses.

In the thermodynamic limit, steps become infinitesimally small, leading to smooth macroscopic responses.

Static chaos arises from infinitely many level crossings as the system size grows.

Abstract

We study statistical properties of peculiar responses in glassy systems at mesoscopic scales based on a class of mean-field spin-glass models which exhibit 1 step replica symmetry breaking. Under variation of a generic external field, a finite-sized sample of such a system exhibits a series of step wise responses which can be regarded as a finger print of the sample. We study in detail the statistical properties of the step structures based on a low temperature expansion approach and a replica approach. The spacings between the steps vanish in the thermodynamic limit so that arbitrary small but finite variation of the field induce infinitely many level crossings in the thermodynamic limit leading to a static chaos effect which yields a self-averaging, smooth macroscopic response. We also note that there is a strong analogy between the problem of step-wise responses in glassy systems at mesoscopic scales and intermittency in turbulent flows due to shocks.