Temperature shifts in the Sinai model: static and dynamical effects

TL;DR

This paper investigates how temperature shifts affect the Sinai model, revealing finite-size effects and rejuvenation phenomena, but showing weaker temperature-dependent separation of scales than in real spin-glasses.

Contribution

It provides an analytical and numerical analysis of temperature effects in the hierarchical Sinai model, highlighting finite-size chaos indicators and rejuvenation effects.

Findings

Finite-size chaos indicators show non-trivial behavior.

Rejuvenation effects are observed at finite times.

Weak separation of time/length scales compared to spin-glasses.

Abstract

We study analytically and numerically the role of temperature shifts in the simplest model where the energy landscape is explicitely hierarchical, namely the Sinai model. This model has both attractive features (there are valleys within valleys in a strict self similar sense), but also one important drawback: there is no phase transition so that the model is, in the large size limit, effectively at zero temperature. We compute various static chaos indicators, that are found to be trivial in the large size limit, but exhibit interesting features for finite sizes. Correspondingly, for finite times, some interesting rejuvenation effects, related to the self similar nature of the potential, are observed. Still, the separation of time scales/length scales with temperatures in this model is much weaker that in experimental spin-glasses.