Nonequilibrium glass transitions in the spherical $p$-spin model with antisymmetric interactions

TL;DR

This paper investigates how antisymmetric, nonreciprocal interactions in the spherical p-spin model affect glassy dynamics, revealing that such interactions generally suppress glass formation and modify the transition point.

Contribution

It introduces and analyzes the effects of antisymmetric interactions in the spherical p-spin model, a novel extension that alters glassy behavior and transition characteristics.

Findings

Antisymmetric interactions suppress glassy behavior.

Analytical expressions for the transition point and order parameter are derived.

Glass transition is shifted and weakened by nonreciprocal interactions.

Abstract

Our theoretical understanding of glassy dynamics is notoriously incomplete, and it is even more so when the glassy systems are driven out of equilibrium. An extreme way to drive a system out of equilibrium is to introduce nonequilibrium dynamics at the microscopic level, e.g., through active forcing of the constituent particles or by having nonreciprocal interactions among the particles. While glassy dynamics under active forcing has been studied by many, the latter nonequilibrium scenario has received little attention. Here, I study the glassy dynamics of the spherical $p$-spin model for $p\geq 3$ with antisymmetric interactions, which generalizes reciprocal interactions in 2-body interactions. The spherical $p$-spin model is an integral tool in the study of dynamical glass transition, and when antisymmetric interactions are added, I show analytically and numerically that glassy behavior is generically suppressed. Moreover, I obtain analytical expressions on the modified dynamical glass transition point and the Edward-Anderson parameter (i.e., the asymptotic plateau height value of the spin-spin correlation function) in the small driving limit.