Inhomogeneous Systems with Unusual Critical Behaviour

Details Inhomogeneous Systems with Unusual Critical Behaviour Inhomogeneous Systems with Unusual Critical Behaviour

1993-12-20

arxiv.org/abs/cond-mat/9312077v2

Adv. Phys. 42 (1993) 683-740

Physics

Condensed Matter

Statistical Mechanics

78 pages, Plain TeX and epsf, 16 postscript-figures

Scientific paper

10.1080/00018739300101544

The phase transitions and critical properties of two types of inhomogeneous 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 couplings deviate from their bulk values according to power laws. In each case the perturbation may be irrelevant, marginal or relevant. In the marginal case one finds local exponents which depend on a parameter. In the relevant case unusual stretched exponential behaviour and/or local first order transitions appear. The discussion combines mean field theory, scaling considerations, conformal transformations and perturbation theory. A number of examples are Ising models for which exact results can be obtained. Some walks and polymer problems are considered, too.

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