SEARCH FOR A SPIN-GLASS PHASE IN FINITE-DIMENSIONAL SPIN MODELS WITH RANDOM MULTISITE INTERACTIONS

We show that in several two-dimensional models with random multisite interactions a spin glass transition cannot occur, since the disorder does not lead to an extensive number of frustrated terms in the Hamiltonian. We perform preliminary Monte Carlo simulations of the (three-dimensional) fcc lattice with random 4-spin interactions among the spins on elementary tetrahedra. The results indicate that either also here a spin glass transition is absent or it is preceded by a dynamical transition, where spin-spin correlations do not decay any more on finite time scales (in the infinite system). This latter scenario would occur with the mean-field result for p-spin interaction spin glasses.