Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spin Glasses on Thin Graphs   In a recent paper we found strong evidence from simulations that the
Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed
amean-field spin glass transition. The intrinsic interest of considering such
random graphs is that they give mean field results without long range
interactions or the drawbacks, arising from boundary problems, of the Bethe
lattice. In this paper we reprise the saddle point calculations for the Ising
and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We
use standard results from bifurcation theory that enable us to treat an
arbitrary number of replicas and any quenched bond distribution. We note the
agreement between the ferromagnetic and spin glass transition temperatures thus
calculated and those derived by analogy with the Bethe lattice, or in previous
replica calculations. We then investigate numerically spin glasses with a plus
or minus J bond distribution for the Ising and Q=3,4,10,50 state Potts models,
paying particular attention to the independence of the spin glass transition
from the fraction of positive and negative bonds in the Ising case and the
qualitative form of the overlap distribution in all the models. The parallels
with infinite range spin glass models in both the analytical calculations and
simulations are pointed out.

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The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: stat