Uniqueness of Ground State in the Edwards-Anderson Spin Glass Model

It is proven rigorously that the ground state in the Edwards-Anderson spin glass model is unique in any dimension for almost all continuous random exchange interactions under a condition that a single spin breaks the global Z(2) symmetry. This theorem implies that replica symmetry breaking does not occur at zero temperature. The site- and bond-overlap are concentrated at their maximal values. Behaviors of short range spin glass models turn out to be much different from those of mean field spin glass models near zero temperature.

Automated summary

It has been rigorously proven that in the Edwards-Anderson spin glass model, the ground state is unique in any dimension for almost all continuous random exchange interactions when a single spin breaks the global Z(2) symmetry. This theorem implies that replica symmetry breaking does not occur at zero temperature, with site- and bond-overlaps concentrated at their maximal values. Short range spin glass models exhibit behaviors near zero temperature that are significantly different from mean field spin glass models.