  We address and resolve the fundamental contradiction that has existed from
the earliest studies on magnetic phase transitions between theoretical models
that ignore the role of thermal vibrations and represent the exchange
interaction as a constant, Jij(0), and analysis of neutron diffraction data
that always incorporates thermal vibrations even though it is also possible to
analyze the same data by ignoring them. Of the two possibilities, ignoring
thermal vibrations in both theoretical models and analysis of diffraction data
leads to the latter giving different magnetic order parameters for different
reciprocal lattice lines. This appears to be the first report of a unique
consequence, viz. the assumption to neglect a physical phenomenon turns a
single-valued experimental observable into a multiple-valued one where all
values are equally valid. This assumption is clearly unacceptable and must be
rejected. The second possibility of incorporating thermal vibrations in both
leads to single-valued theoretical and experimental order parameters. Thus,
analysis of neutron diffraction data constrain the exchange interaction in all
theoretical models to be temperature dependent and represented as Jij(T).
Additional experimental and theoretical evidences in support of this conclusion
are presented.
