Nicoletta Cancrini, Filippo Cesi, Fabio Martinelli
The spectral gap for the Kawasaki dynamics at low temperature
(889K, PS)
ABSTRACT. In this paper we analyze the convergence to equilibrium of
Kawasaki dynamics for the Ising model in the phase coexistence
region. First we show, in strict analogy with the non--conservative
case that in any lattice dimension,
for any boundary condition, any positive temperature and particle density,
the spectral gap in a box of side $L$
does not shrink faster than a negative exponential of the surface $L^{d-1}$.
Then we prove that, in two dimensions and free boundary condition,
the spectral gap in a box of side $L$
is smaller than a negative exponential of $L$ provided that the temperature
is below the critical one and the particle density $\rho$ satisfies
$\r\in(\r_-^*,\r_{+}^*)$, where $\rho^*_{\pm}$
are the particle density of the plus and minus phase respectively.