https://doi.org/10.1007/s100510170221
Metastable states of a ferromagnet on random thin graphs
IRSAMC, Laboratoire de Physique Quantique, Université Paul Sabatier,
118 route de Narbonne, 31062 Toulouse, Cedex 4, France
Corresponding author: a lefevre@irsamc2.ups-tlse.fr
Received:
15
November
2000
Revised:
12
February
2001
Published online: 15 May 2001
We calculate the mean number of metastable states of an Ising ferromagnet on
random thin graphs of fixed connectivity c. We find, as for totally connected
mean field spin
glasses, that this mean increases exponentially with the number of sites,
and is the same as that calculated for the spin glass on the same
graphs. An annealed calculation of the average
number
of
metastable states of energy E per spin
is carried out. For small c, an analytic
result is obtained. These results are compared with the one obtained for
the corresponding
spin glasses, in order to discuss the role played by loops on thin
graphs and hence the effect of real frustration on the distribution of
metastable states.
PACS: 05.20.-y – Classical statistical mechanics / 75.10.Nr – Spin-glass and other random models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001