Dynamical fluctuations in an exactly solvable model of spin glasses

TL;DR

This paper analytically investigates dynamical fluctuations in the low-temperature phase of the exactly solvable $p=2$ spherical spin glass model, revealing a fluctuation dissipation relation and scaling behaviors of four-point functions.

Contribution

It provides an exact calculation of dynamical fluctuations at order 1/N and extends fluctuation dissipation relations to out-of-equilibrium regimes in a solvable spin glass model.

Findings

Derived fluctuation dissipation relation for four-point functions

Identified $t^{-1/2}$ scaling of the out-of-equilibrium fluctuation function

Calculated dynamical fluctuations at order 1/N in the low-temperature phase

Abstract

In this work we calculate the dynamical fluctuations at O(1/N) in the low temperature phase of the $p=2$ spherical spin glass model. We study the large-times asymptotic regimes and we find, in a short time-differences regime, a fluctuation dissipation relation for the four-point correlation functions. This relation can be extended to the out of equilibrium regimes introducing a function $X_{t}$ which, for large time $t$, we find scales as $t^{-1/2}$ as in the case of the two-point functions.