High q-state clock spin glasses in three dimensions and the Lyapunov exponents of chaotic phases and chaotic phase boundaries

İlker, Efe and Berker, A. Nihat (2013) High q-state clock spin glasses in three dimensions and the Lyapunov exponents of chaotic phases and chaotic phase boundaries. Physical Review E, 87 (3). ISSN 1539-3755 (Print) 1550-2376 (Online)

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Official URL: http://dx.doi.org/10.1103/PhysRevE.87.032124


Spin-glass phases and phase transitions for q-state clock models and their q -> infinity limit the XY model, in spatial dimension d = 3, are studied by a detailed renormalization-group study that is exact for the d = 3 hierarchical lattice and approximate for the cubic lattice. In addition to the now well-established chaotic rescaling behavior of the spin-glass phase, each of the two types of spin-glass phase boundaries displays, under renormalization-group trajectories, their own distinctive chaotic behavior. These chaotic renormalization-group trajectories subdivide into two categories, namely as strong-coupling chaos (in the spin-glass phase and, distinctly, on the spin-glass-ferromagnetic phase boundary) and as intermediate-coupling chaos (on the spin-glass-paramagnetic phase boundary). We thus characterize each different phase and phase boundary exhibiting chaos by its distinct Lyapunov exponent, which we calculate. We show that, under renormalization group, chaotic trajectories and fixed distributions are mechanistically and quantitatively equivalent. The phase diagrams of arbitrary even q-state clock spin-glass models in d = 3 are calculated. These models, for all non-infinite q, have a finite-temperature spin-glass phase. Furthermore, the spin-glass phases exhibit a universal ordering behavior, independent of q. The spin-glass phases and the spin-glass-paramagnetic phase boundaries exhibit universal fixed distributions, chaotic trajectories and Lyapunov exponents. In the XY model limit, our calculations indicate a zero-temperature spin-glass phase.

Item Type:Article
Additional Information:Article Number: 032124
ID Code:23880
Deposited By:A. Nihat Berker
Deposited On:24 Jan 2014 09:52
Last Modified:04 Feb 2015 15:11

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