Structure of the liquid-vapor interface using a Gaussian column model with a variable interaction range

We study properties of the liquid-vapor interface using an exactly solvable model consisting of a one-dimensional array of columns whose interaction is of variable range and quadratic in the height difference between columns. In the limit of infinitely long-ranged intercolumn interactions the classical mean-field description of the interface is exact: there is an “intrinsic” interface profile of finite width and all pair correlations are short ranged. However, for realistic short-ranged interactions the model is equivalent to the capillary wave model of Buff, Lovett and Stillinger; here we find long-ranged pair correlations parallel to the interface of precisely the form deduced by Wertheim. The interface profile now depends on system size and strength of an external gravitational field; the interface width diverges as the field tends to zero in an infinite system. Explicit expressions for the pair correlation are inverted to yield the direct correlation function in the interfacial region.