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.