6-Point Tripled Ashkin-Teller Global Phase Diagrams in Two and Three Dimensions

Abstract

The tripled Ashkin-Teller model including 6-point interactions is solved in d = 2 and 3 by renormalization-group theory that is exact on the hierarchical lattice and approximate on the recently first/second-order-transition improved Migdal-Kadanoff procedure. Five different ordered phases occur in the dimensionally distinct global phase diagrams. 16 different phase diagram cross-sections in the 2-point and 4-point interaction space are obtained, with first-and second-order phase transitions, multiple tricritical points and critical endpoints.