Critical Behavior at M-Axial Lifshitz Points

Details Critical Behavior at M-Axial Lifshitz Points Critical Behavior at M-Axial Lifshitz Points

2002-05-14

arxiv.org/abs/cond-mat/0205284v2

Acta physica slovaca 52 (4), 271-283 (2002)

Physics

Condensed Matter

Statistical Mechanics

Latex with 6 eps-files included (figures), to appear in Acta Physica Slovaka (Proceedings of the 5th International Conference

Scientific paper

An introduction to the theory of critical behavior at Lifshitz points is given, and the recent progress made in applying the field-theoretic renormalization group (RG) approach to $\phi^4$ $n$-vector models representing universality classes of $m$-axial Lifshitz points is surveyed. The origins of the difficulties that had hindered a full two-loop RG analysis near the upper critical dimension for more than 20 years and produced long-standing contradictory $\epsilon$-expansion results are discussed. It is outlined how to cope with them. The pivotal role the considered class of continuum models might play in a systematic investigation of anisotropic scale invariance within the context of thermal equilibrium systems is emphasized. This could shed light on the question of whether anisotropic scale invariance implies an even larger invariance, as recently claimed in the literature.

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