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

Abstract

The authors have simulated the Ising 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, they have 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 delta 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, they obtain results in the interior by discarding the two outer shells of the Cayley tree when calculating the thermal averages. For fixed (uncorrelated) boundary conditions, P(q) seems to converge to a delta 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.