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Stiffness exponents for lattice spin glasses in dimensions \(\mathsf{d = 3,\ldots,6}\)

  • S. Boettcher
Article

Abstract.

The stiffness exponents in the glass phase for lattice spin glasses in dimensions \(d = 3,\ldots,6\) are determined. To this end, we consider bond-diluted lattices near the T = 0 glass transition point p *. This transition for discrete bond distributions occurs just above the bond percolation point p c in each dimension. Numerics suggests that both points, p c and p *, seem to share the same 1/d-expansion, at least for several leading orders, each starting with 1/(2d). Hence, these lattice graphs have average connectivities of \(\alpha = 2dp\gtrsim1\) near p * and exact graph-reduction methods become very effective in eliminating recursively all spins of connectivity \(\leq3\), allowing the treatment of lattices of lengths up to L = 30 and with up to 105-106 spins. Using finite-size scaling, data for the defect energy width \(\sigma(\Delta E)\) over a range of p > p * in each dimension can be combined to reach scaling regimes of about one decade in the scaling variable \(L(p-p^*)^{\nu^*}\). Accordingly, unprecedented accuracy is obtained for the stiffness exponents compared to undiluted lattices (p = 1), where scaling is far more limited. Surprisingly, scaling corrections typically are more benign for diluted lattices. We find in \(d = 3,\ldots,6\) for the stiffness exponents y 3 = 0.24(1), y 4 = 0.61(2), y 5 = 0.88(5), and y 6 = 1.1(1).

Keywords

Glass Transition Transition Point Spin Glass Glass Phase Energy Width 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Physics DepartmentEmory UniversityAtlanta, GeorgiaUSA

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