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Ninth Lecture Advanced Statistical Mechanics

was about Landau theory of second-order transitions, a theory that fascinated many generations of students, me including. With no exaggeration, it was the most valueable thing I’ve leaned at university, though, if I recall it correctly, not from the lectures. I wonder if I could convey at least a part of my fascination to the students.

Problem in hand was that one of the important aspects of the fascination is the recognition of the utmost generality of this theory: it can be applied to any type of ordering, to anything and anywhere. The best way to convey this aspect is to illustrate the theory with many and complementary examples and put it in the context of symmetry groups. Kardar is rather half-hearted about this, he lists some examples but basically keeps taking about “magnetization”. He also avoids the discussions of anisotropy of fourth-order terms and any mentioning of irreducible representations in the context of second-order transition. While I could understand his intent to keep things simple, this is rather a castration of Landau theory.

Well, it’s easy to be critical, it’s difficult to talk about these aspects given shot lecture time. I did it by just mentioning symmetries and groups, and considering pyro-electric transition where anisotropy plays an important role. I could put some stress on it letting the students think about possible scenarios of breaking the cubic symmetry. However, I should try to improve on these aspects next year.

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