Stability of thermodynamic and dynamical order in a system of globally coupled rotors
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Publication:5694129
DOI10.1088/0305-4470/38/25/005zbMATH Open1073.82030arXivcond-mat/0506014OpenAlexW3099458135MaRDI QIDQ5694129
Author name not available (Why is that?)
Publication date: 29 September 2005
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/cond-mat/0506014
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