Two connections between random systems and non-Gibbsian measures

TL;DR

This paper explores the relationship between disordered systems and non-Gibbsian measures, highlighting two main roles: as tools for analysis and as subjects of non-Gibbsian properties, with discussions on mean-field and Kac limit approaches.

Contribution

It clarifies the distinction between using disordered systems as tools and as subjects of non-Gibbsian measures, and discusses potential connections via Kac limits.

Findings

Disordered systems serve as analytical tools for non-Gibbsian measures.

Non-Gibbsian properties are observed in measures of quenched disordered systems.

Potential links between finite-range and mean-field non-Gibbsian properties are proposed.

Abstract

In this contribution we discuss the role disordered (or random) systems have played in the study of non-Gibbsian measures. This role has two main aspects, the distinction between which has not always been fully clear: 1) {\em From} disordered systems: Disordered systems can be used as a tool; analogies with, as well as results and methods from the study of random systems can be employed to investigate non-Gibbsian properties of a variety of measures of physical and mathematical interest. 2) {\em Of} disordered systems: Non-Gibbsianness is a property of various (joint) measures describing quenched disordered systems. We discuss and review this distinction and a number of results related to these issues. Moreover, we discuss the mean-field version of the non-Gibbsian property, and present some ideas how a Kac limit approach might connect the finite-range and the mean-field non-Gibbsian properties.