Strange Attractor in the Potts Spin Glass on Hierarchical Lattices

Abstract

The spin-glass $q$-state Potts model on $d$-dimensional diamond hierarchical lattices is investigated by an exact real space renormalization group scheme. Above a critical dimension $d_l(q)$ for $q>2$, the coupling constants probability distribution flows to a low-temperature \emph{strange attractor} or to the high-temperature paramagnetic fixed point, according to the temperature is below or above the critical temperature $T_c(q,d)$. The strange attractor was investigated considering four initial different distributions for $q=3$ and $d=5$ presenting strong robustness in shape and temperature interval suggesting a condensed phase with algebraic decay.

6 pages, 4 figures, to appear in Physics Letters A 2013

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• The Chiral Potts Spin Glass in d=2 and 3 Dimensions
• Phase Transitions between Different Spin-Glass Phases and between Different Chaoses in Quenched Random Chiral Systems
• Devil's Staircase Continuum in the Chiral Clock Spin Glass with Competing Ferromagnetic-Antiferromagnetic and Left-Right Chiral Interactions