Spectroscopy of phase transitions for multiagent systems

TL;DR

This paper investigates phase transitions in multiagent systems by analyzing their linear response, revealing universal behaviors and singularities associated with susceptibility, applicable to both equilibrium and nonequilibrium models.

Contribution

It introduces a method to detect phase transitions in finite multiagent systems through linear response analysis, highlighting universal features independent of specific observables.

Findings

Evidence of susceptibility divergence at phase transitions

Universality of singular behavior across models

Loss of analyticity linked to pole crossing frequencies

Abstract

In this paper we study phase transitions for weakly interacting multiagent systems. By investigating the linear response of a system composed of a finite number of agents, we are able to probe the emergence in the thermodynamic limit of a singular behaviour of the susceptibility. We find clear evidence of the loss of analyticity due to a pole crossing the real axis of frequencies. Such behaviour has a degree of universality, as it does not depend on either the applied forcing nor on the considered observable. We present results relevant for both equilibrium and nonequilibrium phase transitions by studying the Desai-Zwanzig and Bonilla-Casado-Morillo models.