Berlin 2005 – wissenschaftliches Programm

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SYRS: Renormalization and Scaling

SYRS 1: SYRS I

SYRS 1.1: Hauptvortrag

Samstag, 5. März 2005, 08:30–09:00, TU H3010

Anisotropic Scale Invariance in Systems with Boundaries: Bulk and Surface Critical Behavior at Lifshitz Points — •Hans Werner Diehl — Fachbereich Physik, Universität Duisburg-Essen, Campus Essen, D-45117 Essen, Germany

A wealth of physical phenomena, both at thermal equilibrium and away from it, exhibit anisotropic scale invariance: distances along one or several principal axes scale as powers of the distances along the remaining ones. This anisotropy makes such phenomena already in bulk systems much richer and more challenging to study. All the more so, this applies to boundary critical phenomena in anisotropic scale invariant systems. For those, the orientation of a boundary plane matters in an essential way, since the distance from it scales differently, depending on how it is oriented. Critical phenomena at bulk Lifshitz points—multicritical points, at which a disordered phase meets both a homogeneous ordered as well as a modulated ordered phase— provide important examples of such systems. Their bulk universality classes are described by natural generalizations of the standard φ⁴ n-vector model, whose systematic analysis via modern field-theoretic renormalization group methods has been a long-standing challenge ever since their introduction in the 1970s. A survey of recent progress made in this direction for the bulk case is presented. The construction of semi-infinite minimal φ⁴ models representing the universality classes of the various surface transitions at m-axial bulk Lifshitz points for distinct types of surface orientations is explained. Results obtained mostly via dimensionality expansions are given and compared with available Monte Carlo and other results.