Viana-Bray Model Research Articles

Monte Carlo simulations of spin glasses at low temperatures

We report the results of Monte Carlo simulations on several spin-glass models at low temperatures. By using the parallel tempering (exchange Monte Carlo) technique we are able to equilibrate down to low temperatures, for moderate sizes, and hence the data should not be affected by critical fluctuations. Our results for short-range models are consistent with a picture proposed earlier that there are large-scale excitations which cost only a finite energy in the thermodynamic limit, and these excitations have a surface whose fractal dimension is less than the space dimension. For the infinite range Viana-Bray model, our results obtained for a similar number of spins, are consistent with standard replica symmetry breaking.

Nature of the spin glass state.

The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range Sherrington-Kirkpatrick (SK) and Viana-Bray models. Our results for the SK and Viana-Bray models agree with the replica symmetry breaking picture. The data for the short range models fit naturally a picture in which there are large scale excitations which cost a finite energy but whose surface has a fractal dimension, d(s), less than the space dimension d. We also discuss the possible crossover to other behavior at larger length scales than the sizes studied.

Theory of site-disordered magnets

In realistic spinglasses, such as CuMn, AuFe and EuSrS, magnetic atoms are located at random positions. Their couplings are determined by their relative positions. For such systems a field theory is formulated. In certain limits it reduces to the Hopfield model, the Sherrington-Kirkpatrick model, and the Viana-Bray model. The model has a percolation transition, while for RKKY couplings the ``concentration scaling'' T_g proportional to c occurs. Within the Gaussian approximation the Ginzburg-Landau expansion is considered in the clusterglass phase, that is to say, for not too small concentrations. Near special points, the prefactor of the cubic term, or the one of the replica-symmetry- breaking quartic term, may go through zero. Around such points new spin glass phases are found.