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Non-self-averaging in Ising spin glasses and hyperuniversality
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2016 (English)In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, E-ISSN 1550-2376, Vol. 93, no 1, 012118Article in journal (Refereed) PublishedText
Abstract [en]

Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized intersample variance) parameter U-22(T, L) for the spin glass susceptibility [and for higher moments Unn (T, L)] is reported for dimensions 2,3,4,5, and 7. In each dimension d the non-self-averaging parameters in the paramagnetic regime vary with the sample size L and the correlation length xi(T, L) as U-nn(beta, L) = [K-d xi (T, L)/L](d) and so follow a renormalization group law due to Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Empirically, it is found that the Kd values are independent of d to within the statistics. The maximum values [U-nn(T, L)](max) are almost independent of L in each dimension, and remarkably the estimated thermodynamic limit critical [U-nn (T, L)](max) peak values are also practically dimension-independent to within the statistics and so are " hyperuniversal." These results show that the form of the spin-spin correlation function distribution at criticality in the large L limit is independent of dimension within the ISG family. Inspection of published non-self-averaging data for three-dimensional Heisenberg and XY spin glasses the light of the Ising spin glass non-self-averaging results show behavior which appears to be compatible with that expected on a chiral-driven ordering interpretation but incompatible with a spin-driven ordering scenario.

Place, publisher, year, edition, pages
2016. Vol. 93, no 1, 012118
Keyword [en]
Mathematical Analysis, Physics
National Category
Mathematical Analysis
URN: urn:nbn:se:umu:diva-116080DOI: 10.1103/PhysRevE.93.012118ISI: 000367901000011OAI: diva2:902125
Available from: 2016-02-10 Created: 2016-02-08 Last updated: 2016-02-10Bibliographically approved

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Lundow, Per-Håkan
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