Addendum A
Physicists of the beginning of 20th century knew that phase transitions in solid state are not "continuous" in their nature. L. Landau, the original creator of the theory of second-order (continuous) phase transitions, also recognized that fact, but suggested that second-order phase transitions "may also exist". Landau defined second-order phase transitions as the antithesis to first-order, describing the latter as "jump-like rearrangement of the crystal lattice", at which latent heat is absorbed or released, symmetries of two phases are not related, and overheating or overcooling is possible. As for second-order phase transitions, they occur homogeneously, without any overheating or overcooling, at "critical points" where only crystal symmetry changes, but structural change is infinitesimal. Landau left no doubt that his theory is that of second-order phase transitions only.
Leaving alone the theory itself, there were several shortcomings in the Landau presentation:
¨He had not answered the arguments of some contemporaries, Max von Laue among them, that second-order phase transitions cannot exist;
¨ The only examples he used to illustrate second-order phase transitions, NH4Cl and BaTiO3, both turned out to be first order;
¨ Description of first-order phase transitions left false impression that the "jump-like" changes occur simultaneously over the bulk;
¨ It was not specified that the only way first-order phase transitions can occur is nucleation and growth (Sec. 1.2);
¨ He remained silent when other theorists began to further "develop" his theory by violating and distorting the conditions separating the two antipodal types of phase transitions.
In order to properly evaluate the ensuing chain of events, we need to expand on the Landau's characterization of a first-order phase transition (Chapter 2):
it is intrinsically local process which has nothing to do with bulk "critical fluctuations" bringing about an instant overall change at a fixed "critical point"; it starts from nucleation in a crystal defect; nucleation temperature is not a "critical point" and not exactly reproducible; nucleation lags are inevitable (hysteresis); it proceeds by "molecule-by-molecule" rearrangements at interfaces over a temperature range where the two phases coexist. The underlying conclusions are impeccable: (1) there are no first-order phase transitions that are "weak", "almost", or "close to" second-order, for they occur by rearrangement at interfaces, and not homogeneously in the bulk, and (2) in no way first-order phase transitions can be described or approximated as "continuous" and "critical phenomenon" in order to become a subject for statistical mechanics.
The Landau theory initiated an avalanche of theoretical papers and books, presented not as a "theory of second-order phase transitions, but as a "theory of phase transitions"; the first-order ones were either incorporated as a "critical phenomenon" as well, or simply disregarded. The actual Landau position was paid no attention. The available new data that any solid-state phase transition, when carefully investigated, turns out to be first order were ignored. Every ferroelectric phase transition turned out of first order (Sec. 4.2.1). Every ferromagnetic phase transition, including in Fe and Ni, turned out of first order (Sec. 4.2.2, 4.2.3, 4.4, 2.6.8). Every "order-disorder" phase transition turned out of first order (Sec.2.7). Even magnetization proceeds as a first-order phase transition (Sec. 4.13). While there are still claims that one or another phase transition is of second order, not a single well-proven case exists.
The next theoretical step was the "scaling renormalization group" theory of 1970th, completely clear of first-order phase transitions. The understanding existed 40 years ago that phase transitions are "usually" first order, while second order only "may exist" has vanished. It is not to say that the theory in question was necessarily not good: it may have other applications, but it has nothing to do with phase transitions - at least in solid state. Nucleation-and-growth does not need to be described by a "scaling" theory.
The theoretical work did not stop there. As one author recently stated, "the scaling theory of critical phenomena has been successfully extended for classical first order transitions…" [M. A. Continentino, cond-mat/0403274]. To any one who understands the real physical nature of first-order phase transitions, and not only as those exhibiting "jumps", it should be evident that such "extension" cannot be justified (Sec. 1.3).
The next section of the theoretical chain was "quantum phase transitions", put forward in the last decade of the previous century as a specific form of all other ("classical") ones considered "continuous" and "critical phenomenon". The experimental fact that overwhelming majority of solid-state phase transitions has been recognized first order was not mentioned (see ADDENDUM B).
Incorporation of first-order phase transitions into the theory of "quantum" phase transitions followed: once again, the nucleation and crystal growth became a homogeneous process and a "critical phenomenon".
As of today, the last link of the chain is the referred above article by Continentino who applied "scaling ideas to quantum first order transitions", thus creating a conglomeration of utmost scientific falsehood.
To make the above picture more complete, two more theoretical branches are to be mentioned, both oblivious of the fact that first-order phase transitions are a process of nucleation and crystal growth. One, "soft-mode" concept (Sec. 1.6, 1.7), is compatible only with instant (cooperative) phase transitions over the bulk (see ADDENDUM G). The other is the theory of "topological" phase transitions erroneously assuming polymorphs to be somehow related (Sec. 1.4.3, 2.2.2, 2.2.4) and transforming from each other by a kind of displacement/deformation (see ADDENDUM C).
Is there another scientific field in modern science where the theory is so totally wrong?