Leaping in full armour from the inspiration of Gibbs

July 13, 2009

Here is the summary section of a pre-print in arXiv by Leo Kadanoff on phase transitions, which pays rich tributes to Gibbs and condensed matter theorists:

We have focused upon the nature of phase transitions and the mean field theory which describes them. The description of the phase transition “leaped in full
armor” from the inspiration of Gibbs, and his insight that a phase transition is an abrupt change which occurs only in a infinite system. Many years of investigation were given theoretical clothing in a mean eld theory set forward originally by van der Waals. This theory provided a generally satisfactory, but numerically inaccurate, description of the main events which occur in the phase diagrams of typical materials. It explains the various ordering of these materials, and some of the similarities and differences among the materials. It explains the universality of the phase diagrams, so that different materials can have rather similar phase diagrams. It fails to explain why the diagrams are inaccurate near the critical point, exactly the region in which the general formulation of Landau would have them be most accurate. But, Landau’s variational method would be the language for the advances to come.

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