 94407 Cesi F, Martinelli F
 On the Layering Transition of an SOS
Surface Interacting with a Wall. II. The Glauber Dynamics
(83K, TeX)
Dec 23, 94

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We continue our study of the statistical mechanics
of a 2D surface above a fixed
wall and attracted towards it by means of a very weak positive magnetic field
$h$ in the solid on solid (SOS) approximation, when the inverse
temperature $\beta$ is very large.
In particular we consider a Glauber dynamics for the above model
and study the rate of approach to equilibrium in a large cube
with arbitrary boundary conditions. Using the results proved in the first
paper of this series we show that for all
$h\in (h^*_{k+1},h^*_k)$ ($\{h_k^*\}$
being the critical values of the magnetic field found in the previous paper)
the
gap in the spectrum of the generator of the dynamics is bounded away
from zero uniformly in the size of the box and in the
boundary conditions. On
the contrary, for $h\,=\,h_k^*$ and free boundary conditions,
we show that the gap in a cube of side $L$ is bounded from above and
from below by a negative exponential of $L$.
Our results provide a strong indication that, contrarily to
what happens in two dimensions, for the three
dimensional dynamical Ising model in a finite cube at low
temperature and very small positive external field, with boundary
conditions that are opposite to the field on one face of the cube
and are absent (free) on the remaining faces, the rate
of exponential convergence to equilibrium, which is positive in
infinite volume, may go to zero exponentially fast in
the side of the cube.
 Files:
94407.tex