Abstract
The order parameter of an elastic phase transition is a component of the strain tensor and the soft mode is an acoustic phonon. In three-dimensional crystals softening can occur in one- or two-dimensional subspaces, which entails a reduction of the fluctuations. By means of the renormalization group theory it is shown that the critical behaviour is classical for systems with one-dimensional soft sectors like Nb3Sn and NaOH, while logarithmic corrections are found for systems with a two-dimensional soft sector. The theory is applied to materials like KDP, or LaP5O14, where the order parameter is a linear combination of an optic phonon and a shear.