The structure of fluctuations near mean-field critical points and spinodals and its implication for physical processes

TL;DR

This paper investigates the complex structure of fluctuations near critical points and spinodals in mean-field systems, revealing that fluctuations comprise many fundamental clusters with significant physical implications for various phenomena.

Contribution

It introduces the concept of fundamental clusters as the building blocks of fluctuations in mean-field systems, highlighting their physical reality and importance.

Findings

Fluctuations near critical points involve many fundamental clusters.

Fundamental clusters are physical objects, not just mathematical constructs.

Implications for nucleation, spinodal decomposition, and earthquake statistics.

Abstract

We analyze the structure of fluctuations near critical points and spinodals in mean-field and near-mean-field systems. Unlike systems that are non-mean-field, for which a fluctuation can be represented by a single cluster in a properly chosen percolation model, a fluctuation in mean-field and near-mean-field systems consists of a large number of clusters, which we term fundamental clusters. The structure of the latter and the way that they form fluctuations has important physical consequences for phenomena as diverse as nucleation in supercooled liquids, spinodal decomposition and continuous ordering, and the statistical distribution of earthquakes. The effects due to the fundamental clusters implies that they are physical objects and not only mathematical constructs.