Metastable states of Ising models on the honeycomb lattice

We calculate the number of metastable states $N_s$ for Ising spins on the honeycomb lattice with quenched bond disorder; several random-bond distributions are investigated. Neither randomness nor frustration is necessary for a large number of metastable states; in fact, the exponent α defined by $N_s$${=2\mathrm{}}^{\alpha N}$, where N is the number of spins, is greater for the uniform-bond model than for some random-ferromagnet and spin-glass models. We introduce and investigate also the ‘‘bond-glass’’ model in which the bonds (rather than the spins) are the dynamical variables, and the spins are quenched; we obtain the exponent α for the particular case of Ising-like bonds.