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

The stiffness exponents in the glass phase for lattice spin glasses in dimensions $d=3,\ldots,6$ 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 pc in each dimension. Numerics suggests that both points, pc 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 $10^5-10^6$ 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 $y_6=1.1(1)$