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

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 $e^{(3)} \ge -2.204...$.