Chiral Potts Spin Glass in $d=2$ and $3$

The chiral spin-glass Potts system with $q=3$ states is studied in $d=2$ and $3$ by renormalization-group theory.[1] 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 boundaries to ferromagnetic, left- and right-chiral phases show, differently, and unusual, fibrous patchwork (microreentrances) of all four (ferromagnetic, left- and right-chiral, chiral spin-glass) 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 usual ferromagnetic-antiferromagnetic spin-glass systems. In $d=2$, the chiral spin-glass Potts system does not have a spin-glass phase. \\[4pt] [1] T. \c{C}a\u{g}lar and A.N. Berker, Phys. Rev. E \underline{94}, 032121 (2016)