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Spectroscopy of phase transitions for multiagent systems.

Niccolò Zagli1, Valerio Lucarini2, Grigorios A Pavliotis1

  • 1Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.

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|July 9, 2021
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Summary
This summary is machine-generated.

This study reveals universal singular behavior in multiagent systems, indicating a phase transition. We observed a loss of analyticity in susceptibility, crucial for understanding system dynamics.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Weakly interacting multiagent systems exhibit complex behaviors.
  • Understanding phase transitions is key to characterizing system dynamics.
  • Linear response theory provides a framework for analyzing system behavior.

Purpose of the Study:

  • To investigate phase transitions in weakly interacting multiagent systems.
  • To probe the emergence of singular behavior in susceptibility.
  • To analyze universality of observed phenomena.

Main Methods:

  • Investigating the linear response of finite agent systems.
  • Analyzing susceptibility in the thermodynamic limit.
  • Studying Desai-Zwanzig and Bonilla-Casado-Morillo models.

Main Results:

  • Observed a singular behavior in susceptibility, indicating a phase transition.
  • Found evidence of loss of analyticity due to a pole crossing the real axis.
  • Demonstrated universality of this behavior, independent of forcing or observable.

Conclusions:

  • The study confirms a universal mechanism for phase transitions in these systems.
  • Loss of analyticity in susceptibility is a key indicator of emergent behavior.
  • Results are applicable to both equilibrium and nonequilibrium phase transitions.