Eur. Phys. J. B 31, 29-39 (2003)
https://doi.org/10.1140/epjb/e2003-00005-y

Numerical results for ground states of spin glasses on Bethe lattices

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

Corresponding author: ^a 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 ), the Extremal Optimization heuristic is employed which provides high-quality results not only for the ground state energies per spin but also for their entropies . 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 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 at small connectivities. While 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