ISSN:
1434-6036
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1140/epjb/e2004-00102-5
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