Multiscale Complexity of Correlated Gaussians

TL;DR

This paper investigates the multiscale complexity of Gaussian models with continuous spins, revealing universal behaviors related to interaction structures and phase transitions, and demonstrating the measure's utility in analyzing correlated systems.

Contribution

It applies a new multiscale complexity measure to Gaussian spin models, uncovering universal behaviors and oscillations linked to frustration and phase transitions.

Findings

Exponential decay of complexity in non-frustrated systems indicates small-scale fluctuations.

Logarithmic divergence near critical points reflects collective modes.

Oscillations in complexity reveal constraints in frustrated systems.

Abstract

We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity profile. For systems with variables that are not frustrated, an exponential decay of multiscale complexity in the disordered regime shows the presence of small-scale fluctuations, and a logarithmically diverging profile of fixed shape near the critical point describes the spectrum of collective modes. For frustrated variables, oscillations in complexity indicate the presence of global or local constraints. These observations show that the multiscale complexity may be a useful tool for interpreting the underlying structure of systems for which pair correlations can be measured.