AN ISING INTERFACE BETWEEN 2 WALLS - COMPETITION BETWEEN 2 TENDENCIES

We consider a ferromagnetic Ising spin system, consisting of m + 1, d- dimensional, layers with ''-'' boundary condition on the bottom layer and ''+'' on the top layer. When beta is larger than beta(cr), the inv erse critical temperature for the d-dimensional Ising model, the inter face generated by the boundary conditions is expected to be halfway be tween bottom and top, for m odd, and just above or below the middle la yer, for m even (each possibility with probability 1/2). In this paper , we prove the above assertion under the condition that beta greater t han or equal to const . m and partly for beta > beta(cr).