Gibbsianness versus non-Gibbsianness of time-evolved planar rotor models (Q1019613)

The authors considered time-evolved planar rotor systems on \(\mathbb Z^d\), \(d\geq 2\), in the transient regime, evolving with stochastic dynamics and starting from an initial Gibbs measure \(\nu\). The Gibbsian property of the system is investigated for small times \(t\) and arbitrary initial Gibbs measures \(\nu\) under different dynamics and then for small inverse initial temperature and arbitrary times. It is shown that the time-evolved measure \(\nu^t\) is Gibbsian for small \(t\) under infinite- or high-temperature dynamics and arbitrary-temperature initial Gibbs measure, and for any \(t\) for high- or infinite-temperature initial measure. Also it is proved that the Gibbs property will be lost after some time \(t\) for a low-temperature initial measure and infinite-temperature dynamics.