Physics – Mathematical Physics
Scientific paper
2001-05-02
Physics
Mathematical Physics
Scientific paper
10.1007/s002200200605
We consider Ising-spin systems starting from an initial Gibbs measure $\nu$ and evolving under a spin-flip dynamics towards a reversible Gibbs measure $\mu\not=\nu$. Both $\nu$ and $\mu$ 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 $t>0$. (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.
Fernández Raúl
Hollander Frank den
Redig Frank
van Enter Aernout C. D.
No associations
LandOfFree
Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-5115