  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.
