Coexistence of stable limit cycles in a generalized Curie-Weiss model with dissipation

TL;DR

This paper investigates a modified Curie-Weiss model with dissipation, revealing that dissipation can lead to multiple stable limit cycles and complex phase transitions, including self-sustained oscillations at low temperatures.

Contribution

It introduces a dissipative extension to the generalized Curie-Weiss model and demonstrates the emergence of multiple stable limit cycles due to dissipation effects.

Findings

Multiple phase transitions at different critical temperatures.

Existence of several stable limit cycles in certain regimes.

Self-sustained periodic behavior at low temperatures.

Abstract

In this paper, we modify the Langevin dynamics associated to the generalized Curie-Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site distribution, the dynamics in the thermodynamic limit can be described by a finite set of ODEs. Depending on the form of the interaction function, the system can have several phase transitions at different critical temperatures. Because of the dissipation effect, not only the magnetization of the systems displays a self-sustained periodic behavior at sufficiently low temperature, but, in certain regimes, any (finite) number of stable limit cycles can exist. We explore some of these peculiarities with explicit examples.