  The dielectric and magnetic polarizations of quantum paraelectrics and
paramagnetic materials have in many cases been found to initially increase with
increasing thermal disorder and hence exhibit peaks as a function of
temperature. A quantitative description of these examples of
'order-by-disorder' phenomenona has remained elusive in nearly ferromagnetic
metals and in dielectrics on the border of displacive ferroelectric
transitions. Here we present an experimental study of the evolution of the
dielectric susceptibility peak as a function of pressure in the nearly
ferroelectric material, strontium titanate, which reveals that the peak
position collapses towards absolute zero as the ferroelectric quantum critical
point is approached. We show that this behaviour can be described in detail
without the use of adjustable parameters in terms of the
Larkin-Khmelnitskii-Shneerson-Rechester (LKSR) theory, first introduced nearly
50 years ago, of the hybridization of polar and acoustic modes in quantum
paraelectrics, in contrast to alternative models that have been proposed. Our
study allows us to construct for the first time a detailed temperature-pressure
phase diagram of a material on the border of a ferroelectric quantum critical
point comprising ferroelectric, quantum critical paraelectric and hybridized
polar-acoustic regimes. Furthermore, at the lowest temperatures, below the
susceptibility maximum, we observe a new regime characterized by a linear
temperature dependence of the inverse susceptibility that differs sharply from
the quartic temperature dependence predicted by the LKSR theory. We find that
this non-LKSR low temperature regime cannot be accounted for in terms of any
detailed model reported in the literature, and its interpretation poses a new
empirical and conceptual challenge.
