The ground state energy per site of the quantum and classical Edwards-Anderson spin-glass model in the thermodynamic limit

TL;DR

This paper establishes rigorous lower bounds for the average ground-state energy per site in the quantum and classical Edwards-Anderson spin-glass models for dimensions 2 and 3, providing new theoretical insights into these complex systems.

Contribution

The paper introduces new rigorous lower bounds for the ground-state energy per site in both quantum and classical Edwards-Anderson models in 2D and 3D.

Findings

Classical model lower bound in 2D: -1.5

Classical model lower bound in 3D: approximately -2.204

Provides theoretical benchmarks for ground-state energies

Abstract

We derive rigorous lower bounds for the average ground-state energy per site $e^{(d)}$ of the quantum and classical Edwards-Anderson spin-glass model in dimensions $d = 2$ and $d = 3$ in the thermodynamic limit. For the classical model they imply that $e^{(2)} \ge -3/2$ and $e^{(3)} \ge -2.204...$.