Second-order phase transitions, L. Landau and his successors

Abstract:

There are only two ways for solid-state phase transitions to be compliant with thermodynamics: emerging of infinitesimal quantity of the new phase, or infinitesimal "qualitative" change occurring uniformly throughout the bulk at a time. The suggested theories of phase transitions are checked here for that compliance and in historical perspective. While introducing the theory of "continuous" second-order phase transitions, L. Landau claimed that they "may also exist" along with the majority of first order phase transitions, the latter being "discontinuous", displaying "jumps" of their physical properties; the fundamental differences between the two types were specified. But his theoretical successors disregarded these irreconcilable differences, incorrectly presenting all phase transitions as a cooperative phenomenon treatable by statistical mechanics. In the meantime, evidence has been mounted that all phase transitions have a nucleation-and-growth mechanism, thus making the above classification unneeded.

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https://arxiv.org/ftp/arxiv/papers/1102/1102.1085.pdf

1. Compliance with thermodynamics 

 Physicists in the beginning of 20th century knew that phase transitions in solid state are not "continuous" in nature. But starting from 1930's the idea of "continuous" phase transitions emerged.

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2. Second-order phase transitions: 

"may also exist" Landau [4-6] developed a theory of second-order phase transitions. But he emphasized that transitions between different crystal modifications are "usually" first-order, occurring by sudden rearrangement of the crystal lattice at which the state of the matter changes abruptly, latent heat is absorbed or released, symmetries of the phases are not related and overheating or overcooling is possible. As for second-order phase transitions, they "may also exist", but no incontrovertible evidence of their existence was presented. It should be noted that expression that something "may exist" implicitly allows it not exist either. In case second-order phase transitions do exist, they must occur homogeneously, without any overheating or overcooling, at "critical points" where only the crystal symmetry changes, but structural change is infinitesimal. Landau left no doubt that his theory is that of second-order phase transitions only.