Eur. Phys. J. B 38, 83-91 (2004)
https://doi.org/10.1140/epjb/e2004-00102-5

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

Physics Department, Emory University, Atlanta, Georgia 30322, USA

Corresponding author: ^a sboettc@emory.edu

Received: 29 October 2003
Published online: 20 April 2004

Abstract

The stiffness exponents in the glass phase for lattice spin glasses in dimensions 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 near p^* and exact graph-reduction methods become very effective in eliminating recursively all spins of connectivity , allowing the treatment of lattices of lengths up to L=30 and with up to spins. Using finite-size scaling, data for the defect energy width over a range of in each dimension can be combined to reach scaling regimes of about one decade in the scaling variable . 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 for the stiffness exponents , , , and .