Spectroscopy of phase transitions for multiagent systems.

  title={Spectroscopy of phase transitions for multiagent systems.},
  author={Niccol{\`o} Zagli and Valerio Lucarini and Grigorios A. Pavliotis},
  volume={31 6},
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… 
2 Citations

Figures from this paper

On some aspects of the response to stochastic and deterministic forcings

The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background



Response theory and phase transitions for the thermodynamic limit of interacting identical systems

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions.

Noisy Hegselmann-Krause Systems: Phase Transition and the 2R-Conjecture

The effects of noise in the continuous-time version of the Hegselmann-Krause model as described by its mean-field Fokker-Planck equation are investigated and the existence of a forbidden zone for the disordered phase to emerge is derived.

An update on the nonequilibrium linear response

The unique fluctuation–dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is ‘analytic’, which,

Critical dynamics and fluctuations for a mean-field model of cooperative behavior

The main objective of this paper is to examine in some detail the dynamics and fluctuations in the critical situation for a simple model exhibiting bistable macroscopic behavior. The model under

Self-synchronization of populations of nonlinear oscillators in the thermodynamic limit

A population of identical nonlinear oscillators, subject to random forces and coupled via a mean-field interaction, is studied in the thermodynamic limit. The model presents a nonequilibrium phase

On the Diffusive-Mean Field Limit for Weakly Interacting Diffusions Exhibiting Phase Transitions

The objective of this article is to analyse the statistical behaviour of a large number of weakly interacting diffusion processes evolving under the influence of a periodic interaction potential. We

On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems.

The general formalism of generalized fluctuation-dissipation relations is illustrated with some examples in nonstandard cases, including driven granular media, systems with a multiscale structure, active matter, and systems showing anomalous diffusion.

Resonances of chaotic dynamical systems.

  • Ruelle
  • Physics
    Physical review letters
  • 1986
It appears desirable to analyze the decay of correlation functions and the possible analyticity of power spectra for physical time evolutions, and for computer generated simple dynamical systems (non-Axiom-A in general).

The Kuramoto model: A simple paradigm for synchronization phenomena

Synchronization phenomena in large populations of interacting elements are the subject of intense research efforts in physical, biological, chemical, and social systems. A successful approach to the

Linear response for macroscopic observables in high-dimensional systems.

A comprehensive picture is presented for the linear response of macroscopic observables in high-dimensional coupled deterministic dynamical systems, where the coupling is via a mean field and the microscopic subsystems may or may not obey linear response theory.