Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Results for Ground States of Spin Glasses on Bethe Lattices   The average ground state energy and entropy for +/- J spin glasses on Bethe
lattices of connectivities k+1=3...,26 at T=0 are approximated numerically. To
obtain sufficient accuracy for large system sizes (up to n=2048), the Extremal
Optimization heuristic is employed which provides high-quality results not only
for the ground state energies per spin e_{k+1} but also for their entropies
s_{k+1}. The results show considerable quantitative differences between
lattices of even and odd connectivities. The results for the 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, e_{k+1} = E_{SK}
sqrt(k+1) - {2E_{SK}+sqrt(2)} / sqrt(k+1), where E_{SK} = -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 find
non-zero entropies s_{k+1} at small connectivities. While s_{k+1} seems to
vanish asymptotically with 1/(k+1) for even connectivities, it is
indistinguishable from zero already for odd k+1 >= 9.

5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th