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

Ising models on the plane square lattice with an arbitrary variation of the bond strengths, J(parallel-to)(z) and J(perpendicular-to)(z), with one of the two axial coordinates, z, are considered. The total entropy 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 local expression provides an effective, variational principle for the free energy and energy-density profiles. In the scaling limit the problem reduces to a set of independent second-order differential equations for each epsilon(q)(z). The power of the method is demonstrated by application to an interface between two uniform but distinct regions; this includes the problem of a wall with a surface field, h1, as a special case. Previous results for the bulk and surface exponents and for the energy-energy correlation function are easily recovered. Near criticality the method yields, in addition, universal, scaled energy-density profiles, epsilon(z;T), which exhibit rich crossovers and nonmonotonic variation with z.