INHOMOGENEOUS SYSTEMS WITH UNUSUAL CRITICAL-BEHAVIOR

The phase transitions and critical properties of two types of inhomoge neous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are considered as well as general parabolic shapes. In the other case the system contains defects, either narrow ones in the form of lines or stars, or extended ones where the couplin gs deviate from their bulk values according to power laws. In each cas e the perturbation may be irrelevant, marginal or relevant. In the mar ginal case one finds local exponents which depend on a parameter. In t he relevant case unusual stretched exponential behaviour and/or local first-order transitions appear. The discussion combines mean field the ory, scaling considerations, conformal transformations and perturbatio n theory. A number of examples are Ising models for which exact result s can be obtained. Some walks and polymer problems are considered, too .