2-DIMENSIONAL LAYERED ISING-MODELS - EXACT VARIATIONAL FORMULATION AND ANALYSIS

Ising models on the plane square lattice with an arbitrary variation o f the bond strengths, J(parallel-to)(z) and J(perpendicular-to)(z), wi th one of the two axial coordinates, z, are considered. The total entr opy is exactly represented as a functional of contributions epsilon(q) (z) to the local energy density arising from the Onsager fermions with wave vector q parallel to the layer axis, y. The resulting explicit l ocal expression provides an effective, variational principle for the f ree energy and energy-density profiles. In the scaling limit the probl em reduces to a set of independent second-order differential equations for each epsilon(q)(z). The power of the method is demonstrated by ap plication to an interface between two uniform but distinct regions; th is includes the problem of a wall with a surface field, h1, as a speci al case. Previous results for the bulk and surface exponents and for t he energy-energy correlation function are easily recovered. Near criti cality the method yields, in addition, universal, scaled energy-densit y profiles, epsilon(z;T), which exhibit rich crossovers and nonmonoton ic variation with z.