Surface terms on the Nishimori line of the Gaussian Edwards-Anderson model

TL;DR

This paper derives integral representations for surface terms in the Gaussian Edwards-Anderson model on the Nishimori line, analyzing their behavior and establishing the existence of the adjacency pressure in the thermodynamic limit.

Contribution

It provides explicit integral formulas for surface terms and proves the thermodynamic limit existence of the adjacency pressure in the Edwards-Anderson model.

Findings

Surface terms are proportional to surface size.

Explicit integral representations for surface pressure are obtained.

Existence of the adjacency pressure in the thermodynamic limit is proven.

Abstract

For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic boundary conditions and the adjacency pressure, i.e., the difference between the pressure of a box and the sum of the pressures of adjacent sub-boxes in which the box can been decomposed. We show that all those terms indeed behave proportionally to the surface size and prove the existence in the thermodynamic limit of the adjacency pressure.