Analysis of the Migdal transformation for models with planar spins on a two-dimensional lattice

By numerical and analytical investigations we show that the bond-moving transformation of Migdal for planar spins on a two-dimensional lattice possesses a very rich structure. We find an infinite hierarchy of one-, three- and higher-dimensional fixed spaces. In addition to phase transitions of the Kosterlitz-Thouless-type, we find Ising-like transitions, for which the critical exponents are the same as those of the q-state Potts model in the Migdal approximation. These critical exponents are constant within each fixed space. The phase diagram is constructed for two specially chosen potentials.