Local optima of the Sherrington-Kirkpatrick Hamiltonian

TL;DR

This paper analyzes the local optima of the Sherrington-Kirkpatrick Hamiltonian, calculating their expected quantity and typical energy levels to understand the energy landscape of this spin glass model.

Contribution

It provides a precise computation of the expected number of local optima and characterizes their typical Hamiltonian values, advancing understanding of the model's energy landscape.

Findings

Expected number of local optima computed

Typical Hamiltonian value determined

Insights into the energy landscape of the model

Abstract

We study local optima of the Hamiltonian of the Sherrington-Kirkpatrick model. We compute the exponent of the expected number of local optima and determine the "typical" value of the Hamiltonian.