Basins of attraction of metastable states of the spherical $p$-spin model

TL;DR

This paper investigates the size and structure of basins of attraction for metastable states in the spherical p-spin model, revealing how initial conditions influence the basin size and connecting these findings to an effective potential framework.

Contribution

It introduces a new analysis of basin sizes in the spherical p-spin model based on initial conditions and links these results to an effective potential approach.

Findings

Finite basin sizes when initial conditions are Boltzmann-weighted.

Vanishing basins with white initial condition weighting.

Connection established between basin structure and effective potential.

Abstract

We study the basins of attraction of metastable states in the spherical $p$-spin spin glass model, starting the relaxation dynamics at a given distance from a thermalized condition. Weighting the initial condition with the Boltzmann distribution we find a finite size for the basins. On the contrary, a white weighting of the initial condition implies vanishing basins of attraction. We make the corresponding of our results with the ones of a recently constructed effective potential.