Exponential relaxation of Glauber dynamics
with some special boundary conditions
Abstract
We consider attractive finite-range Glauber dynamics and show that
if a certain mixing condition is satisfied, then
the system evolving on arbitrary subsets of the lattice,
with appropriate boundary conditions, converges to
equilibrium exponentially fast, in the uniform sense, uniformly
over the subsets of the lattice. This result applies, for instance,
to the ferromagnetic nearest neighbor Ising model in the so called
``Basuev region'', where complete analyticity is expected to fail.
Technically the result in this paper is an extension of a result
of Martinelli and Olivieri, who proved that under a weaker form of
mixing the infinite system approaches equilibrium exponentially
fast.
Conceptually this paper may be seen as a step towards
developing and exploiting a restricted notion of complete analyticity
in which the boundary conditions, rather than the shapes of
the regions under consideration are being restricted.
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