# Spectroscopy of phase transitions for multiagent systems.

@article{Zagli2021SpectroscopyOP, title={Spectroscopy of phase transitions for multiagent systems.}, author={Niccol{\`o} Zagli and Valerio Lucarini and Grigorios A. Pavliotis}, journal={Chaos}, year={2021}, volume={31 6}, pages={ 061103 } }

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

### On some aspects of the response to stochastic and deterministic forcings

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2022

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…

## References

SHOWING 1-10 OF 70 REFERENCES

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

- PhysicsProceedings of the Royal Society A
- 2020

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

- Physics2016 IEEE 55th Conference on Decision and Control (CDC)
- 2016

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

- Mathematics
- 2013

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

- Mathematics
- 1983

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

- Physics
- 1987

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

- MathematicsArchive for Rational Mechanics and Analysis
- 2021

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.

- PhysicsChaos
- 2019

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.

- PhysicsPhysical 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

- Physics
- 2005

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.

- PhysicsChaos
- 2019

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.