Loss and Recovery of Gibbsianness for XY models in external fields

Abstract

We consider planar rotors (XY spins) in ${\mathbb{Z}}^d$, starting from an initial Gibbs measure and evolving with infinite-temperature stochastic (diffusive) dynamics. At intermediate times, if the system starts at low temperature, Gibbsianness can be lost. Due to the influence of the external initial field, Gibbsianness can be recovered after large finite times. We prove some results supporting this picture.

14 pages, 2 figures

References in corpus (1)

• Disorder versus the Mermin-Wagner-Hohenberg effect: From classical spin systems to ultracold atomic gases

Cited by in corpus (1)

• Classical spin models with broken symmetry: Random Field Induced Order and Persistence of spontaneous magnetization in presence of a random field