Free energy according to Poincare' and Landau
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The Mathematics of Liquid Crystals
In the Landau theory of phase transitions one considers an effective potential U whose symmetry group G and degree d depend on the system under consideration; generally speaking, U is the most general Ginvariant polynomial of degree d. When such a U turns out to be too complicate for a direct analysis, it is essential to be able to drop unessential terms, i.e., to apply a simplifying criterion. Criteria based on singularity theory exist and have a rigorous foundation, but are often very difficult to apply in practice. Here we consider a simplifying criterion and rigorously justify it on the basis of classical LiePoincare theory; this builds on (and justifies) a proposal by Gufan.
This talk is part of the Isaac Newton Institute Seminar Series series.
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