The ground state energy of the mean field spin glass model
Flora Koukiou (LPTM)
TL;DR
This paper calculates the limiting free energy of the Sherrington-Kirkpatrick spin glass model at low temperature, providing a lower bound for the ground state energy close to known theoretical and numerical values.
Contribution
It introduces a method based on a functional equation of Gibbs measures to determine the free energy and ground state energy bounds for the spin glass model.
Findings
Lower bound for ground state energy: -0.7833
Close to replica symmetry breaking predictions
Aligns with numerical simulation results
Abstract
From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the ground state energy \[\epsilon_0\geq -0.7833\cdots,\] close to the replica symmetry breaking and numerical simulations values.
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Taxonomy
TopicsTheoretical and Computational Physics · Complex Network Analysis Techniques · Stochastic processes and statistical mechanics