Spectroscopy of phase transitions for multiagent systems

Zagli, N. ORCID: https://orcid.org/0000-0003-4509-1615, Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471 and Pavliotis, G. A. ORCID: https://orcid.org/0000-0002-3468-9227 (2021) Spectroscopy of phase transitions for multiagent systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 31 (6). 061103. ISSN 1089-7682 doi: 10.1063/5.0053558

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/98674
Item Type	Article
Refereed	Yes
Divisions	Interdisciplinary Research Centres (IDRCs) > Centre for the Mathematics of Planet Earth (CMPE) Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	American Institute of Physics
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