Temperature chaos in some spherical mixed $p$-spin models

TL;DR

This paper demonstrates that certain spherical mixed even-$p$-spin models exhibit temperature chaos, showing that small perturbations can induce chaos even where pure models do not, expanding understanding of spin glass behavior.

Contribution

The paper provides new examples of spherical mixed even-$p$-spin models that exhibit temperature chaos, contrasting with previous results on pure models and highlighting the impact of perturbations.

Findings

Temperature chaos occurs in some spherical mixed $p$-spin models.

Small perturbations induce chaos even in models where pure models lack it.

Results extend understanding of spin glass models and their sensitivity to temperature changes.

Abstract

We give two types of examples of the spherical mixed even-$p$-spin models for which chaos in temperature holds. These complement some known results for the spherical pure $p$-spin models and for models with Ising spins. For example, in contrast to a recent result of Subag who showed absence of chaos in temperature in the spherical pure $p$-spin models for $p\geq 3$, we show that even a smaller order perturbation induces temperature chaos.