Global Ashkin-Teller Phase Diagrams in Two and Three Dimensions: Multicritical Bifurcation versus Double Tricriticality Endpoint

TL;DR

This paper explores the phase diagrams of the Ashkin-Teller model in two and three dimensions using renormalization-group theory, revealing complex multicritical behaviors and phase transition types.

Contribution

It provides a detailed analysis of the Ashkin-Teller phase diagrams in 2D and 3D, highlighting the differences in multicritical points and phase transition structures.

Findings

Identification of three ordered phases in both dimensions.

Observation of bifurcation points in 2D phase transitions.

Detection of tricritical and critical endpoints in 3D.

Abstract

The global phase diagrams of the Askin-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.