Metastable states of a ferromagnet on random thin graphs

Abstract:

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 ±J spin glass on the same graphs. An annealed calculation of the average number <N _MS(E)> 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 ±J 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.