Loss and Recovery of Gibbsianness for XY models in external fields

TL;DR

This paper studies the evolution of XY spin models under stochastic dynamics, showing how Gibbsianness can be lost and later recovered due to external fields, with theoretical results supporting this behavior.

Contribution

It provides rigorous results demonstrating the loss and recovery of Gibbsianness in XY models influenced by external fields during stochastic evolution.

Findings

Gibbsianness can be lost at intermediate times starting from low temperature.

External fields can induce recovery of Gibbsianness after large finite times.

Theoretical evidence supports the dynamic transition in Gibbsianness properties.

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.