Multiple Particle Correlation Analysis of Many-Particle Systems: Formalism and Application to Active Matter

TL;DR

This paper presents a rapid analysis method for multi-particle correlations in many-particle systems, applied to active matter, revealing the importance of higher-order correlations and introducing a new way to identify phase transitions.

Contribution

It introduces a fast spatial point pattern analysis technique for multi-particle correlations and demonstrates its effectiveness on the Vicsek model of active matter.

Findings

Multi-particle correlations are significant even in disordered phases.

Two-particle correlation parameter effectively detects phase transitions.

Correlation analysis provides detailed phase space insights.

Abstract

We introduce a fast spatial point pattern analysis technique which is suitable for systems of many identical particles giving rise to multi-particle correlations up to arbitrary order. The obtained correlation parameters allow to quantify the quality of mean field assumptions or theories that incorporate correlations of limited order. We study the Vicsek model of self-propelled particles and create a correlation map marking the required correlation order for each point in phase space incorporating up to ten-particle correlations. We find that multi-particle correlations are important even in a large part of the disordered phase. Furthermore, the two-particle correlation parameter serves as an excellent order parameter to locate both phase transitions of the system, whereas two different order parameters were required before.