The Chiral Potts Spin Glass in d=2 and 3 Dimensions

Abstract

The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking concentration c, with determination of phase chaos and phase-boundary chaos. In d=3, the system has ferromagnetic, left-chiral, right-chiral, chiral spin-glass, and disordered phases. The phase boundaries to the ferromagnetic, left- and right-chiral phases show, differently, an unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left-chiral, right-chiral, chiral spin-glass) ordered ordered phases, especially in the multicritical region. The chaotic behavior of the interactions, under scale change, are determined in the chiral spin-glass phase and on the boundary between the chiral spin-glass and disordered phases, showing Lyapunov exponents in magnitudes reversed from the usual ferromagnetic-antiferromagnetic spin-glass systems. At low temperatures, the boundaries of the left- and right-chiral phases become thresholded in p and c. In the d=2, the chiral spin-glass system does not have a spin-glass phase, consistently with the lower-critical dimension of ferromagnetic-antiferromagnetic spin glasses. The left- and right-chirally ordered phases show reentrance in chirality concentration p.

9 pages, 7 figures, 19 phase diagrams. Final published version

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• Multifractal Spin-Glass Chaos Projection and Interrelation of Multicultural Music and Brain Signals
• Phase Transitions between Different Spin-Glass Phases and between Different Chaoses in Quenched Random Chiral Systems
• First-Order to Second-Order Phase Transition Changeover and Latent Heats of q-State Potts Models in d=2,3 from a Simple Migdal-Kadanoff Adaptation
• Lower-Critical Dimension of the Random-Field XY Model and the Zero-Temperature Critical Line
• Renormalization-Group Theory of the Heisenberg Model in d Dimensions
• Nematic Ordering in the Heisenberg Spin-Glass System in d=3 Dimensions
• Spin-s Spin-Glass Phases in the d=3 Ising Model
• XY-Ashkin-Teller Phase Diagram in d=3