The Dobrushin-Hryniv Theory for the Two-Dimensional Lattice Widom-Rowlinson Model

Abstract

We consider the fluctuation of the phase boundary separating two phases of the Widom-Rowlinson model in the plane square lattice. The phase boundary is conditioned to have specified values of the area underneath and the height difference of two end points. Dobrushin and Hryniv studied the phase boundary of the Solid-on-Solid model [DH1] and of the Ising model [DH2], and obtained the central limit theorem for the fluctuation of the phase boundary from the Wulff profile. The phase boundary of the Ising model is well approximated by that of the Solid-on-Solid model with the aid of the cluster expansion. Their argument seems to be applicable to the general models which have polymer representation. We apply their theory to the Widom-Rowlinson model.