- 07-295 A.C.D. van Enter and W.M.Ruszel
- Gibbsianness versus non-Gibbsianness of time-evolved planar rotor models
Nov 24, 07
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Abstract. We study the Gibbsian character of time-evolved planar rotor systems on
Z^d, in the transient regime, evolving with stochastic dynamics and starting from an initial Gibbs measure \nu. We model the system by interacting Brownian diffusions moving on circles. We prove that for small times 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-temeprature dynamics there is a time interval(t_0, t_1) such that \nu^t fails to be Gibbsian in d=2.