Thermodynamic Limit for Finite Dimensional Classical and Quantum Disordered Systems

TL;DR

This paper presents a straightforward proof for the existence of the thermodynamic limit of quenched specific pressure in classical and quantum disordered systems, including spin glasses, using Jensen's inequality.

Contribution

It introduces a simple, general method based on Jensen's inequality to establish the thermodynamic limit for disordered systems with minimal assumptions.

Findings

Proves the existence of the thermodynamic limit for classical and quantum disordered systems.

Applicable to systems with any disorder distribution satisfying stability.

Simplifies previous proofs by relying on basic inequalities.

Abstract

We provide a very simple proof for the existence of the thermodynamic limit for the quenched specific pressure for classical and quantum disordered systems on a $d$-dimensional lattice, including spin glasses. We develop a method which relies simply on Jensen's inequality and which works for any disorder distribution with the only condition (stability) that the quenched specific pressure is bounded.