  The critical fluctuations in SrTiO$_3$ near its $105 K$ structural phase
transition were studied with triple axis diffractometry using high energy ($\ge
100 keV$) synchrotron radiation in different SrTiO$_3$ crystals with different
oxygen vacancy concentrations. Due to the presence of oxygen vacancies the
critical behaviour is changed compared to defect-free systems. In our
experiments a smearing out of the squared order parameter and a crossover of
the critical exponents $\nu$ and $\gamma$ above the phase transition
temperature is observed, with the crossover temperature strongly depending on
the concentration of the defects. To understand the experimental findings, e.g.
the unusual values for the critical exponents found near the critical
temperature, the Ginzburg-Landau-Wilson functional for structural phase
transitions in disordered systems was analyzed using renormalization group
theory and the replica trick. Considering the effects of defects which locally
increase the transition temperature leads to a qualitative understanding of the
observed behaviour. The crossover behaviour of the critical exponents can be
modeled and a quantitative analysis of the observed experimental data is
presented.
