Criticality and the Onset of Ordering in the Standard Vicsek Model

TL;DR

This paper reviews recent studies on the Standard Vicsek Model, highlighting its critical phase transition behavior, finite-size scaling, dynamical properties, and connections to XY spin models, to better understand collective animal behavior.

Contribution

It provides a comprehensive analysis of the phase transition in the SVM, including finite-size scaling, dynamical exponents, and network analysis, linking flocking to XY spin models.

Findings

Identification of continuous phase transition in SVM

Finite-size scaling and critical exponents characterized

Network analysis reveals onset of order similar to XY models

Abstract

Experimental observations of animal collective behavior have shown stunning evidence for the emergence of large-scale cooperative phenomena resembling phase transitions in physical systems. Indeed, quantitative studies have found scale-free correlations and critical behavior consistent with the occurrence of continuous, second-order phase transitions. The Standard Vicsek Model (SVM), a minimal model of self-propelled particles in which their tendency to align with each other competes with perturbations controlled by a noise term, appears to capture the essential ingredients of critical flocking phenomena. In this paper, we review recent finite-size scaling and dynamical studies of the SVM, which present a full characterization of the continuous phase transition through dynamical and critical exponents. We also present a complex network analysis of SVM flocks and discuss the onset of ordering in connection with XY-like spin models.