Stiffness exponents for lattice spin glasses in dimensions d = 3,...,6
Physics Department, Emory University, Atlanta, Georgia
Corresponding author: a email@example.com
Published online: 20 April 2004
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 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 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 .
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 64.60.Cn – Order-disorder transformations; statistical mechanics of model systems / 75.10.Nr – Spin-glass and other random models / 02.60.Pn – Numerical optimization
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004