Dimensional crossover and absence of quantum criticality in SrTi16O1-x18Ox

The isotope-induced ferroelectricity observed in SrTi(18)O(3) (STO18) enables a systematic study of the crossover between quantum paraelectricity and ferroelectricity as a function of x in SrTi(16)O(1-x)(18)O(x) (STO16(1-x)STO18(x)). We predict that all ferroelectric compounds have a finite transition temperature T(c) and show a dimensionality crossover from d=3 to d=4 at sufficiently low temperature. A discontinuity in behavior takes place around x=0.35, where quantum fluctuations suppress the transition. No evidence is found for a quantum critical point in the phase diagram. The high temperature structural transition shows a substantial isotope dependence which is, however, less striking than for the ferroelectric transition.