Spreading of Damage in the SK Spherical Spin Glass

TL;DR

This paper investigates the Langevin dynamics of the spherical SK spin glass, revealing a dynamical transition in the asymptotic distance between replicas that correlates with the static phase transition, highlighting complex aging phenomena.

Contribution

It provides a novel analysis of the asymptotic behavior of two replicas in the spherical SK model, linking dynamical and static phase transitions.

Findings

Asymptotic distance is maximal for closely initialized replicas.

A dynamical transition occurs at the static phase transition temperature.

The model exhibits non-trivial aging phenomena.

Abstract

By considering the Langevin dynamics of the SK spin glass with a spherical constraint we calculate the asymptotic distance between two real replicas that evolve with the same thermal noise from different initial conditions. Despite the simplicity of the model its dynamics is known to be non trivial and presents aging phenomena. We find that the asymptotic distance between two replicas is maximal for a whole family of initial conditions that are arbitrarily close at t=0 . The asymptotic distance presents a dynamical transition at a temperature equal to the static phase transition one.