Stiffness exponents for lattice spin glasses in dimensions d=3, ... ,6

The stiffness exponents in the glass phase for lattice spin glasses in dimensions d=3,...,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=2dpgreater than or similar to1 near p* and exact graph-reduction methods become very effective in eliminating recursively all spins of connectivity less than or equal to3, allowing the treatment of lattices of lengths up to L = 30 and with up to 10(5)-10(6) spins. Using finite-size scaling, data for the defect energy width sigma(DeltaE) 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,...,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).