Large time zero temperature dynamics of the spherical p=2-spin glass model of finite size

TL;DR

This paper investigates the long-time zero-temperature dynamics of a finite-size spherical p=2-spin glass model, revealing that near-extreme eigenvalues govern observable behaviors and that decay exponents are universal and exactly computable.

Contribution

It provides an exact analysis of the late-time dynamics of the finite-size spherical p=2-spin glass, highlighting the role of near-extreme eigenvalues and universal decay exponents.

Findings

Observable dynamics are governed by near-extreme eigenvalues.

Decay exponents at late times are universal and exactly derived.

Behavior is non self-averaging due to finite size effects.

Abstract

We revisit the long time dynamics of the spherical fully connected $p = 2$-spin glass model when the number of spins $N$ is large but {\it finite}. At $T=0$ where the system is in a (trivial) spin-glass phase, and on long time scale $t \gtrsim {\cal O}{(N^{2/3})}$ we show that the behavior of physical observables, like the energy, correlation and response functions, is controlled by the density of near-extreme eigenvalues at the edge of the spectrum of the coupling matrix $J$, and are thus non self-averaging. We show that the late time decay of these observables, once averaged over the disorder, is controlled by new universal exponents which we compute exactly.