https://doi.org/10.1007/s100510051151
Metastable states of spin glasses on random thin graphs
IRSAMC, Laboratoire de Physique
Quantique, Université Paul Sabatier,
118 route de Narbonne,
31062 Toulouse Cedex, France
Received:
14
October
1999
Revised:
14
December
1999
Published online: 15 June 2000
In this paper we calculate the mean number of metastable states
for spin glasses on so called random thin graphs with couplings taken from
a symmetric binary distribution .
Thin graphs are graphs where the local connectivity of each site is fixed to
some value c. As in totally connected mean field models we find that the
number of metastable states increases exponentially with the system size.
Furthermore we find that the average number of metastable states
decreases as c in agreement with previous studies showing that finite
connectivity corrections of order 1/c increase the number of metastable
states with respect to the totally connected mean field limit.
We also prove that the average number of metastable states in the limit
is finite and converges to the average number of metastable
states in the Sherrington-Kirkpatrick model. An annealed calculation for
the number of metastable states
of energy E is also carried
out giving a lower bound on the ground state energy of these spin glasses.
For small c one may obtain analytic expressions for
.
PACS: 05.20.-y – Classical statistical mechanics / 75.10.Nr – Spin glasses and other random models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000