A constrained TAP approach for disordered spin models: application to the mixed spherical case

TL;DR

This paper investigates the metastability and temperature chaos in mixed spherical spin models, introducing a constrained TAP approach to better understand low-temperature dynamics and improve initial condition treatments.

Contribution

It develops a constrained TAP framework for disordered spin models, offering new insights into metastability and relaxation dynamics at low temperatures.

Findings

Confirmed temperature chaos in a broad temperature range

Modified TAP free energy with overlap constraints

Provided clues for improving low-temperature relaxation analysis

Abstract

We revisit the metastability properties of the mixed p-spin spherical disordered models. Firstly, using known methods, we show that there is temperature chaos in a broad range of temperatures. Secondly, we modify the definition of the Thouless-Anderson-Palmer free energy density by including constraints that enforce a chosen overlap between the searched metastable states and another reference state, that could be a characteristic one of a different temperature. We argue that this refined analysis provides clues to understand the weird behaviour of the low temperature relaxation dynamics of these models, and suggests ways to improve the treatment of the initial conditions to overcome the difficulties encountered so far.