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Gibbsianness versus non-Gibbsianness of time-evolved planar rotor models

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  • van Enter, A.C.D.
  • Ruszel, W.M.

Abstract

We study the Gibbsian character of time-evolved planar rotor systems (that is, systems which have two-component, classical XY, spins) on , d>=2, in the transient regime, evolving with stochastic dynamics and starting from an initial Gibbs measure [nu]. We model the system with interacting Brownian diffusions moving on circles. We prove that for small times t and arbitrary initial Gibbs measures [nu], or for long times and both high- or infinite-temperature initial measure and dynamics, the evolved measure [nu]t stays Gibbsian. Furthermore, we show that for a low-temperature initial measure [nu] evolving under infinite-temperature dynamics there is a time interval (t0,t1) such that [nu]t fails to be Gibbsian for d>=2.

Suggested Citation

  • van Enter, A.C.D. & Ruszel, W.M., 2009. "Gibbsianness versus non-Gibbsianness of time-evolved planar rotor models," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1866-1888, June.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:6:p:1866-1888
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    Cited by:

    1. Lacker, Daniel & Ramanan, Kavita & Wu, Ruoyu, 2021. "Locally interacting diffusions as Markov random fields on path space," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 81-114.

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