  The low temperature acoustic and thermal properties of amorphous, glassy
materials are remarkably similar. All these properties are described
theoretically with reasonable quantitative accuracy by assuming that the
amorphous solid contains dynamical defects that can be described at low
temperatures as an ensemble of two-level systems (TLS), but the deep nature of
these TLSs is not clarified yet. Moreover, glassy properties were found also in
disordered crystals, quasicrystals, and even perfect crystals with a large
number of atoms in the unit cell. In crystals, the glassy properties are not
universal, like in amorphous materials, and also exhibit anisotropy. Recently
it was proposed a model for the interaction of two-level systems with arbitrary
strain fields (Phys. Rev. B 75, 64202, 2007), which was used to calculate the
thermal properties of nanoscopic membranes at low temperatures. The model is
also suitable for the description of anisotropic crystals. We describe here the
results of the calculation of anisotropic glass-like properties in crystals of
various lattice symmetries, emphasizing the tetragonal symmetry.
