The isotope-induced ferroelectricity observed in SrTi 18 O 3 ͑STO18͒ enables a systematic study of the crossover between quantum paraelectricity and ferroelectricity as a function of x in SrTi 16 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. SrTi 16 O 3 has been known for more than 50 years and is one of the best investigated perovskite oxides. Around T s = 105 K a structural instability takes place which is accompanied by the freezing of a zone-boundary mode. 1,2 Simultaneously, a long-wavelength optic mode decreases in energy and is reminiscent of a ferroelectric instability. 3 An extrapolation of its frequency to zero suggests a ferroelectric phasetransition temperature of T c = 17 K. This instability does not take place, however, since quantum fluctuations set in and dominate the low-temperature dynamical properties. In this regime, temperature is an inappropriate parameter for a phase diagram and the dielectric properties. As a consequence the system was termed a "quantum paraelectric." 4 An analogous behavior is observed in KTaO 3 ͑Ref. 5͒ and CaTiO 3 . 6 In all these compounds ferroelectricity can be induced by sufficient doping. In SrTi 16 O 3 ͑STO16͒ Ca doping leads to finite values of T c , and an interesting crossover from a XY n = 2 quantum ferroelectric to a random field-induced domain state takes place with increased Ca doping. 7 Another route to inducing ferroelectricity in STO16 has recently been realized by replacing 16 O by its isotope 18 O. 8 Here, the instability takes place at T c = 24 K and both phases, the ferroelectric and the paraelectric ones, have subsequently been investigated in detail. 9 While long-wavelength probes such as Raman scattering or infrared studies provide evidence for a purely displacive transition with perfect mode softening, 10,11 local probes such as NMR or EPR support an order/disorder-driven phase transition. 12 That both dynamics can coexist has been shown theoretically, and this can resolve the apparent experimental controversy. 13 The higher temperature structural phase transition has been the focus of detailed experimental investigations, since it was early suggested that also here order/disorder and displacive dynamics accompany this instability. 14-16 In particular, a two component approach was developed, since a central peak emerges upon approaching T s which increases in intensity with decreasing temperature. 15,16 An explanation of this observation has been given in terms of intrinsic or quenched defects, 17,18 intrinsic effects, and quasistatic domains, 19,20 and recently been shown to be intrinsic. 11 ...