Boundary Critical Behaviour of Two-Dimensional Layered Ising Models

Abstract

Layered models are models in which the coupling constants depend in an arbitrary way on one spatial coordinate, usually the distance from a free surface or boundary. Here the theory of the boundary critical behaviour of two-dimensional layered Ising models, including the Hilhorst–van Leeuwen model and models for aperiodic systems, is reviewed, with a particular attention to exact results for the critical behaviour and the boundary order parameter.