Document 
Eur. Phys. J. B 31, 29-39 (2003)
DOI: 10.1140/epjb/e2003-00005-y
Numerical results for ground states of spin glasses on Bethe lattices
S. BoettcherPhysics Department, Emory University, Atlanta, Georgia 30322, USA sboettc@emory.edu
(Received 9 August 2002 Published online 27 January 2003)
Abstract
The average ground state energy and entropy for
spin glasses
on Bethe lattices of connectivities
at
T=0 are
approximated numerically. To obtain sufficient accuracy for large
system sizes (up to
n=212), the Extremal Optimization heuristic
is employed which provides high-quality results not only for the
ground state energies per spin
ek+1 but also for their entropies
sk+1. The results indicate sizable differences between lattices
of even and odd connectivities. The extrapolated ground state energies
compare very well with recent one-step replica symmetry breaking
calculations. These energies can be scaled for all even
connectivities
k+1 to within a fraction of a percent onto a simple
functional form,
, where
ESK=-0.7633 is the ground state energy for the broken replica
symmetry in the Sherrington-Kirkpatrick model. But this form is in
conflict with perturbative calculations at large
k+1, which do not
distinguish between even and odd connectivities. We also find non-zero
entropies per spin
sk+1 at small connectivities. While
sk+1
seems to vanish asymptotically with
1/(k+1) for even connectivities,
it is numerically indistinguishable from zero already for odd
.
05.10.-a Computational methods in statistical physics and nonlinear dynamics
75.10.Nr - Spin-glass and other random models.
02.60.Pn - Numerical optimization.
89.75.-k - Complex systems.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2003