Monotonicity and Thermodynamic Limit for Short Range Disordered Models

TL;DR

This paper proves that for short-range Gaussian disordered models, the quenched thermodynamic limit is achieved monotonically when the variance of the potential scales with volume.

Contribution

It establishes a monotonicity property of the thermodynamic limit in short-range Gaussian disordered models based on variance growth.

Findings

Thermodynamic limit is monotonic with volume growth.

Variance growth proportional to volume ensures convergence.

Provides theoretical foundation for disordered model analysis.

Abstract

If the variance of a short range Gaussian random potential grows like the volume its quenched thermodynamic limit is reached monotonically.