Spectroscopy of phase transitions for multiagent systems
File(s)
Accepted version
Author(s)
Zagli, Niccolo
Lucarini, Valerio
Pavliotis, Grigorios A
Type
Journal Article
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 behavior of the susceptibility. We find clear evidence of the loss of analyticity due to a pole crossing the real axis of frequencies. Such behavior has a degree of universality, as it does not depend on either the applied forcing or 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.
Multiagent models feature in a very vast range of applications in natural sciences, social sciences, and engineering. We study here the Desai–Zwanzig (DZ) and Bonilla–Casado–Morillo (BCM) models, which are paradigmatic for equilibrium and nonequilibrium conditions, respectively. Phase transitions result from the coordination between the individual agents and are associated with the divergence of the linear response of the system. The occurrence of phase transitions is universal: it does not depend on the acting forcing and can be detected by looking at virtually any observable of the system. We showcase here how response theory is capable of providing a useful angle for understanding the universal properties of phase transitions in complex systems.
Multiagent models feature in a very vast range of applications in natural sciences, social sciences, and engineering. We study here the Desai–Zwanzig (DZ) and Bonilla–Casado–Morillo (BCM) models, which are paradigmatic for equilibrium and nonequilibrium conditions, respectively. Phase transitions result from the coordination between the individual agents and are associated with the divergence of the linear response of the system. The occurrence of phase transitions is universal: it does not depend on the acting forcing and can be detected by looking at virtually any observable of the system. We showcase here how response theory is capable of providing a useful angle for understanding the universal properties of phase transitions in complex systems.
Date Issued
2021-06-03
Date Acceptance
2021-05-01
Citation
Chaos: an interdisciplinary journal of nonlinear science, 2021, 31 (6), pp.1-8
ISSN
1054-1500
Publisher
American Institute of Physics
Start Page
1
End Page
8
Journal / Book Title
Chaos: an interdisciplinary journal of nonlinear science
Volume
31
Issue
6
Copyright Statement
© 2021 Author(s). This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Chaos 31, 061103 (2021); https://doi.org/10.1063/5.0053558
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000657468400001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
EP/P031587/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Physics, Mathematical
Mathematics
Physics
LINEAR-RESPONSE THEORY
MEAN-FIELD MODEL
FLUCTUATION-DISSIPATION
STATISTICAL-MECHANICS
NONLINEAR OSCILLATORS
SYNCHRONIZATION
NONEQUILIBRIUM
CONVERGENCE
EQUILIBRIUM
DYNAMICS
Publication Status
Published
Article Number
ARTN 061103
Date Publish Online
2021-06-03