01-200 A.C.D. van Enter, R. Fern\'andez, F. den Hollander, F. Redig
Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures (531K, gzipped postscript) May 30, 01
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We consider Ising-spin systems starting from an initial Gibbs measure $\nu$ and evolving under a spin-flip dynamics towards a reversible Gibbs measure $\mu neq \nu$. Both $\mu$ and $\nu$ are assumed to have a finite-range interaction. We study the Gibbsian character of the measure $\nu S(t)$ at time t and show the following: (1) For all $\nu$ and $\mu$, $\nu S(t)$ is Gibbs for small t. (2)If both $\nu$ and $\mu$ have a high or infinite temperature, then $\nu S(t)$ is Gibbs for all $t \geq 0$. (3) If \nu$has a low non-zero temperature and a zero magnetic field and$\mu$has a high or infinite temperature, then$\nu S(t)$is Gibbs for small t and non-Gibbs for large t. (4) If$\nu$has a low non-zero temperature and a non-zero magnetic field and$\mu$has a high or infinite temperature, then$\nu S(t)$is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where$\mu\$ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios.

Files: 01-200.src( 01-200.keywords , EFHRlast.ps )