Bond-moving transformations for continuous-spin systems

We consider two- and three-dimensional lattices with on each lattice a D-dimensional classical spin-vector. We restrict ourselves to nearest neighbour interactions which only depend on the angle between the spin-vectors. For these systems the bond-moving approximation of Migdal and Kadanoff is used to derive renormalisation group equations which do not violate the symmetry of the lattice. Without further approximations these equations are then solved numerically. In addition to the specific heat we also calculate critical temperatures, critical exponents and phase diagrams for ferromagnets, liquid crystals and other related systems. For the simple cubic lattice we find a rich phase diagram, which among others indicates the existence of an anti-nematic phase in liquid crystals.