Spin-Glass Phases and Multichaos in the Ashkin-Teller Model

TL;DR

This paper explores the complex phase diagram of the Ashkin-Teller spin glass in three dimensions, revealing multiple phases, chaotic behavior, and unique reentrant phenomena using renormalization-group theory.

Contribution

It provides the first detailed phase diagram of the 3D Ashkin-Teller spin glass, identifying new spin-glass phases and reentrant behavior through exact and approximate renormalization-group calculations.

Findings

Identification of two distinct chaotic spin-glass phases.

Discovery of phase reentrance opposite to previous spin-glass diagrams.

Seven different phases including ferromagnetic, antiferromagnetic, and entropic states.

Abstract

The global phase diagram of the Ashkin-Teller spin glass is calculated in d = 3 spatial dimensions by renormalization-group theory. Depending on the value of the positive or negative four-spin interaction, qualitatively different topologies are found for the spin-glass phase diagram in the usual variables of temperature and fraction of antiferromagnetic nearest-neighbor interactions. Two different spin-glass phases occur. Both spin-glass phases are chaotic. One spin-glass exhibits phase reentrance that is reverse from the reentrances seen in previous spin-glass phase diagrams. Seven different phases: Ferromagnetic and antiferromagnetic, entropic ferromagnetic and entropic antiferromagnetic, spin-glass and entropic spin-glass, and disordered phases occur. The entropic ferromagnetic phase unusually but understandably occurs at temperatures above one spin-glass phase. A random disorder line is identified and no phase transition occurs on this lie. Our calculation is exact on the d = 3 hierarchical lattice and Migdal-Kadanoff approximate on the cubic lattice.