Talk:Landau theory
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Add a figure
[edit]I think we should add a picture of many landau curves at different temperatures for a simple curve like f = a + b*m^2 + c*m^3 + d*m^4 and show how the metastable/stable ordered state is formed, to increase the obvious link to phase transitions.
The figure that is on top now does not look like a simple landau expansion and does not say what curve is plotted.
LotteUU (talk) 11:30, 16 November 2021 (UTC)
comment
[edit]Actually, I only made up the fact that the critical exponents for liquid-gas at T_c and ferromagnets at T_c were known to be the same. This fact, while true, may have been established much later after Landau's theory (something like 1937). However, it would seem Landau had to have proposed this theory, in light of the many other existing theories, for a special reason. And the phenomenon of universality would have been sufficient motivation to give weight to this theory, which exploited basic features of the system such as symmetries and analyticity. I acknowledge that this paragraph requires fact checking. Wilgamesh 22:43, 18 Sep 2004 (UTC)
Good content, obscure name
[edit]I quite like the content of this article but think that the title choice could be improved. I was curious to look at the article because Landau had so many theories that I didn't know which one to expect! The best course of action I can think of would be to move the article to "second-order phase transition" and to plan to add other content later. BTW, I note that Phase_transition doesn't link here although it should. Alison Chaiken 04:38, 15 January 2006 (UTC)
- Although he may have had many theories, I think this might be the only one explicitly called "Landau Theory." At least, so it is named in my statistical mechanics text books. If there are other theories actually called "Landau Theory" then we might need disambiguation, but I don't think this page should be moved. --Starwed 00:32, 7 March 2006 (UTC)
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Not (quantitatively) valid close to critical point
[edit]"Given these two conditions, one can write down (in the vicinity of the critical temperature, Tc) a phenomenological expression for the free energy as a Taylor expansion in the order parameter." This is something the article says about the Landau free energy. However, the Landau free energy is generally not valid close to the critical point and any information it gives on behaviour of the system around the critical point need not be correct (like the critical exponents it predicts). This is already indicated by the fact that the Landau free energy is a Taylor expansion in the order parameter. Therefore it is an expansion of the free energy around the disordered phase (order parameter = 0), so this approximation is best in the vicinity of the disordered phase, instead of the vicinity of the critical temperature. An274 (talk) 19:52, 6 December 2021 (UTC)
== Cited references
Not sure why we link to Yukhnovskii, I R, Phase Transitions of the Second Order – Collective Variables Method. There are a ton of good classic books on stat mech and landau theory. I've never heard of this one. It is out of print AND obscure. Possibly the author added the link? — Preceding unsigned comment added by 86.14.201.34 (talk) 14:50, 6 October 2023 (UTC)