Energy Landscape of the Finite-Size Mean-field 3-Spin Spherical Model

TL;DR

This paper investigates the energy landscape of a finite-size mean-field 3-spin spherical model, identifying stationary points and analyzing glass transition properties, bridging finite systems and the thermodynamic limit.

Contribution

It provides a comprehensive numerical analysis of all stationary points for small system sizes using polynomial homotopy continuation, linking finite and infinite system behaviors.

Findings

All stationary points identified for systems up to 20 spins.

Finite-size complexity measures compared to thermodynamic limit.

Insights into glass transition phenomena from finite-system analysis.

Abstract

We study the 3-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial homotopy continuation method. On the basis of these stationary points, we analyze the complexity and other quantities related to the glass transition of the model and compare these finite-system quantities to their exact counterparts in the thermodynamic limit.