Saray, A.Berker, A.N.2025-11-152025-11-1520260960-0779https://doi.org/10.1016/j.chaos.2025.117458The 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 line. Our calculation is exact on the d = 3 hierarchical lattice and Migdal–Kadanoff approximate on the cubic lattice. © 2025 Elsevier Ltd.eninfo:eu-repo/semantics/closedAccessAshkin–Teller Spin-Glass in D=3Chaotic Renormalization-Group TrajectoriesEntropic Ferromagnetism and AntiferromagnetismQualitatively Different Phase Diagram TopologiesRenormalization-Group TheoryTwo Different Chaotic Spin-Glasses, Lyapunov ExponentsArticle10.1016/j.chaos.2025.1174582-s2.0-105022212890