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.