Chiral Spin Glasses, Chaos, and Spin-Glass Lower-Critical Dimension from Continuously Variable Dimensional Realizations

The numerically exact renormalization-group studies of spin glasses on hierarchical lattices continues to yield surprising new results. In this talk, we shall concentrate on two such results: (1) An entirely new type of spin-glass, resulting from only competing chiral interactions (in the absence of ferromagnetic-antiferromagnetic competition). (2) A lower lower-critical spin-glass dimension, resulting from the invention of continuously variable spatial dimensionality in hierarchical lattices. The chiral clock spin-glass model with q = 5 states, with both competing ferromagnetic-antiferromagnetic and left-right chiral frustrations, is studied in d = 3 spatial dimensions by renormalization-group theory.[1] The global phase diagram is calculated in temperature, antiferromagnetic bond concentration p, random chirality strength, and right-chirality concentration c. The system has a ferromagnetic phase, a multitude of different chiral phases, a chiral spin-glass phase, and a critical (algebraically) ordered phase. The ferromagnetic and chiral phases accumulate at the disordered phase boundary and form a spectrum of devil’s staircases, where different ordered phases characteristically intercede at all scales of phase-diagram space. Shallow and deep reentrances of the disordered phase, bordered by fragments of regular and temperature-inverted devil’s staircases, are seen. The extremely rich phase diagrams are presented as continuously and qualitatively changing videos. By quenched-randomly mixing local units of different spatial dimensionalities, we have studied Ising spinglass systems on hierarchical lattices continuously in dimensionalities 1 <=d >=3.[2] The global phase diagram in temperature, antiferromagnetic bond concentration, and spatial dimensionality is calculated. We find that, as dimension is lowered, the spin-glass phase disappears to zero temperature at the lower-critical dimension dc = 2.431. Our system being a physically realizable system, this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As dimension is lowered towards dc, the spin-glass critical temperature continuously goes to zero, but the spin-glass chaos fully subsists to the brink of the disappearance of the spin-glass phase. The Lyapunov exponent, measuring the strength of chaos, is thus largely unaffected by the approach to dc and shows a discontinuity to zero at dc.
[1] T. Çağlar and A.N. Berker, Phys. Rev. E 96, 032103, 1-6 (2017).
[2] B. Atalay and A.N. Berker, Phys. Rev. E 98, 042125, 1-5 (2018).