Stability of thermodynamic and dynamical order in a system of globally coupled rotors

TL;DR

This paper investigates the stability and order in globally coupled rotors within microcanonical and canonical ensembles, revealing ensemble inequivalence and the conditions under which dynamical order emerges.

Contribution

It provides a unified analysis of stationary and non-stationary solutions, including stability properties, in a system of coupled rotors with ferromagnetic and antiferromagnetic interactions.

Findings

Canonical distribution is stable at low temperatures in ferromagnetic systems.

Non-stationary solutions exhibit neutral stability below critical temperatures.

Antiferromagnetic systems show neutral stability for all solutions across temperatures.

Abstract

A system of globally coupled rotors is studied in a unified framework of microcanonical and canonical ensembles. We consider the Fokker-Planck equation governing the time evolution of the system, and examine various stationary as well as non-stationary solutions. The canonical distribution, describing equilibrium, provides a stationary solution also in the microcanonical ensemble, which leads to order in a system with ferromagnetic coupling at low temperatures. On the other hand, the microcanonical ensemble admits additional stationary and non-stationary solutions; the latter allows dynamical order, characterized by multiple degrees of clustering, for both ferromagnetic and antiferromagnetic interactions. We present a detailed stability analysis of these solutions: In a ferromagnetic system, the canonical distribution is observed stable down to a certain temperature, which tends to get lower as the number of Fourier components of the perturbed distribution is increased in the analysis. The non-stationary solution remains neutrally stable below the critical temperature, indicating inequivalence between the two ensembles. For antiferromagnetic systems, all solutions are found to be neutrally stable at all temperatures, suggesting that dynamical ordering is relatively easy to observe at low temperatures compared with ferromagnetic systems.