Possible Loss and Recovery of GibbsiannessDuring the Stochastic Evolution of Gibbs Measures
Abstract
We consider Isingspin systems starting from an initial Gibbs measure $\nu$ and evolving under a spinflip dynamics towards a reversible Gibbs measure $\mu\not=\nu$. Both $\nu$ and $\mu$ are assumed to have a finiterange 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 $t>0$. (3) If $\nu$ has a low nonzero temperature and a zero magnetic field and $\mu$ has a high or infinite temperature, then $\nu S(t)$ is Gibbs for small $t$ and nonGibbs for large $t$. (4) If $\nu$ has a low nonzero temperature and a nonzero magnetic field and $\mu$ has a high or infinite temperature, then $\nu S(t)$ is Gibbs for small $t$, nonGibbs 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 2002
 DOI:
 10.1007/s002200200605
 arXiv:
 arXiv:mathph/0105001
 Bibcode:
 2002CMaPh.226..101V
 Keywords:

 Mathematical Physics;
 Mathematics  Probability;
 82C22;
 60K35
 EPrint:
 doi:10.1007/s002200200605