Document 
Eur. Phys. J. B 38, 83-91 (2004)
DOI: 10.1140/epjb/e2004-00102-5
Stiffness exponents for lattice spin glasses in dimensions
S. Boettcher Physics Department, Emory University, Atlanta, Georgia 30322, USA 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
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
105-106 spins. Using finite-size scaling, data
for the defect energy width
over a range of
p>p*
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
y3=0.24(1),
y4=0.61(2),
y5=0.88(5), and
y6=1.1(1).
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