Spectroscopy of phase transitions for multiagent systems

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