Ising spin glass on a D = 3 hierarchical lattice: Effects of tailed coupling distributions |
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Authors: | Fernando D. Nobre Constantino Tsallis |
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Affiliation: | a Departamento de Física Teórica e Experimental, UFRN, Campus Universitário, C.P. 1641, 59072-970, Natal, RN, Brazil b Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud, 150, 22290-180, Rio de Janeiro, RJ, Brazil |
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Abstract: | Within a real-space renormalization-group framework, we approach the cubic lattice through a D = 3 diamond-like hierarchical lattice. The model is a standard, nearest-neighbor, Ising spin glass with coupling constants {Jij} distributed according to the family of continuous probability distributions Pq(Jij) ∝ 1/[1 + (q − 1)Jij2/2J2]1/(q − 1) (if 1 + (q − 1) Jij2/2J2 > 0, and zero otherwise; q ). Such distributions, which arise naturally in the treatment, within the recently proposed nonextensive thermostatistics, of anomalous diffusion, reproduce the usual, Gaussian case, for q → 1. Moreover, they present a second moment Jij2 proportional to (5 − 3q)−1 for q < 5/3, diverging for q ≥ 5/3, but keeping a finite width at midheight. In the limit q → 3, Pq(Jij) collapses with the abscissa, and so the width at midheight diverges. We compute the q-dependence of the spin-glass critical temperature Tc. We show numerically that Tc does not scale with Jij21/2 (contrary to the usual belief), but rather with the width at midheight of Pq(Jij). Our results suggest that Tc vanishes as −1/q when q → −∞; furthermore, we verified that Tc diverges exponentially when q approaches 3 from below. |
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Keywords: | Spin Glasses Renormalization group Nonextensive thermodynamics |
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