Ordinary fully occupied low-temperature Gaussian Edwards–Anderson model

Determine, separately by spatial dimension and at each fixed finite inverse temperature, whether boundary-response mixing holds for the ordinary fully occupied Gaussian Edwards–Anderson half-space specifications; if it fails, identify a weaker condition that ensures selector independence of the weighted boundary response and controls the normal-depth limit; and determine whether that condition implies a full-sequence regular-cube free-to-fixed surface limit. At zero temperature, establish separately a response formula and the interchange of the volume and temperature limits.

Background

The paper establishes finite-depth tangential pressure limits and, under boundary-response mixing, proves selector independence of the weighted one-spin boundary response together with exponential convergence as the slab depth increases. It also obtains regular-rectangle surface limits under a bounded Dobrushin condition and verifies mixing in a subcritical disagreement regime.

These results do not cover the ordinary fully occupied Gaussian Edwards–Anderson model at sufficiently low temperature: Gaussian couplings are unbounded, the bounded Dobrushin theorem is unavailable, and the disagreement parameter approaches one as the inverse temperature grows. Although compactness and metastate methods provide subsequential DLR states and finite-volume Gaussian interpolation identities are available, the paper identifies normal localization and a corresponding full-sequence surface limit as unresolved issues. The zero-temperature response formula and interchange of volume and temperature limits are stated as requiring separate arguments.