Global Ashkin-Teller phase diagrams in two and three dimensions: Multicritical bifurcation versus double tricriticality-endpoint

Abstract

The global phase diagrams of the Ashkin-Teller model are calculated in d = 2 and 3 by renormalization-group theory that is exact on the hierarchical lattice and approximate on the recently improved Migdal-Kadanoff procedure. Three different ordered phases occur in the dimensionally distinct phase diagrams that reflect three-fold order-parameter permutation symmetry, a closed symmetry line, and a quasi-disorder line. First- and second-order phase boundaries are obtained. In d = 2, second-order phase transitions meeting at a bifurcation point are seen. In d = 3, first- and second-order phase transitions are separated by tricritical and critical endpoints.