ON THE 2-DIMENSIONAL STOCHASTIC ISING-MODEL IN THE PHASE COEXISTENCE REGION NEAR THE CRITICAL-POINT

We consider the two-dimensional stochastic Ising model in finite squar e Lambda with free boundary conditions, at inverse temperature beta > beta(c) and zero external field. Using duality and recent results of I offe on the Wulff construction close to the critical temperature, we e xtend some of the results obtained by Martinelli in the low-temperatur e regime to any temperature below the critical one. In particular we s how that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side leng th of Lambda, with a rate constant determined by the surface tension a long one of the coordinate axes. We also extend to the same range of t emperatures the result due to Shlosman on the equilibrium large deviat ions of the magnetization with free boundary conditions.