99-272 Nicoletta Cancrini, Filippo Cesi, Fabio Martinelli

The spectral gap for the Kawasaki dynamics at low temperature (889K, PS) Jul 16, 99

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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.

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