On the Surface Pressure for the Edwards-Anderson Model

TL;DR

This paper introduces a new integral representation for surface pressure in the Edwards-Anderson model, providing bounds and analyzing its behavior at high temperature, revealing it remains non-zero.

Contribution

It presents a novel integral representation for surface pressure and establishes bounds, advancing understanding of surface effects in spin glass models.

Findings

Surface pressure can be expressed via a quenched bond-overlap integral.

Bounds on surface pressure are uniform across volumes.

Surface pressure remains non-zero at high temperature.

Abstract

For the Edwards-Anderson model we introduce an integral representation for the surface pressure (per unit surface) in terms of a quenched moment of the bond-overlap on the surface. We find upper and lower bounds uniformly in the volume and show that at high temperature its value is strictly different from zero.