Monte Carlo simulations of the Ising spin glass on lattices with finite connectivity

E simulated the king spin-glass model on a random lattice with a finite (average) coordination number and also on the Bethe lattice with various different boundary conditions.In particular, we calculated the overlap function P(q) for two independent samples.For the random lattice, the results are consistent with a spin-glass transition above which P(q) converges to a Dirac S function for large N (number of sites) and below which P(q) has in addition a long tail similar to previous results obtained for the infinite-range model.For the Bethe lattice, we obtain results in the interior by discarding the two outer shells of the Cayley tree when calculating the thermal averages. Forfixed (uncorrelated) boundary conditions, P ( q ) seems to converge to a S function even below the spin-glass transition whereas on a closed lattice (correlated boundary conditions) P(q) has a long tail similar to its behaviour in the random-lattice case.