Chiral spin glasses, continuum of devil's staircases, and thresholded roughening from frozen impurities
Çağlar, Tolga (2017) Chiral spin glasses, continuum of devil's staircases, and thresholded roughening from frozen impurities. [Thesis]
The roughening phase diagram of the three-dimensional Ising model with uniaxially anisotropic interactions is calculated for the entire range of anisotropy, using hard-spin mean-field theory. Quenched random pinning centers and missing bonds on the interface of isotropic and anisotropic Ising models show domain boundary roughening that exhibits consecutive thresholding transitions as a function of interaction anisotropy. Quenched random chirality is introduced and investigated using renormalization-group theory for three examples: The global phase diagram of 3−state chiral Potts spin glass with competing left-right chiral interactions is obtained for chirality concentration, chirality breaking concentration and temperature, showing a new spin-glass phase. An unusual fibrous patchwork of microreentrances of all four (ferromagnetic, left chiral, right chiral, chiral spin glass) ordered phases is seen. The spin-glass phase boundary to disordered phase shows, unusually, more chaotic behavior than the chiral spin-glass phase itself. The q−state chiral clock double spin-glass model has competing left-right chiral and ferromagnetic-antiferromagnetic interactions. The global phase diagram is obtained for antiferromagnetic bond concentration, chirality-breaking concentration, random chirality strength, and temperature. The global phase diagram for q = 5 includes a ferromagnetic, a multitude of chiral phases with different pitches, a chiral spin glass, an algebraically ordered critical phases. The ferromagnetic and chiral phases intercede with each other to form a widely varying continuum of Devil’s staircase structures. The global phase diagram for q = 4 shows, four different spin-glass phases, including conventional, chiral, and quadrupolar spin-glass phases, and phase transitions between spin-glass phases. Chaotic behaviors are measured through Lyapunov exponents.
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