Squared interaction matrix Sherrington-Kirkpatrick model for a spin glass

The mean-field theory of a spin glass with a specific form of nearest- and next-nearest-neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we find either the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one-step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

Collective dynamic properties in simple crystals: Influence of the structural disorder

Collective dynamic properties in Lennard-Jones crystals are investigated by molecular dynamics simulation. The study is focused on properties such as the dynamic structure factors, the longitudinal and transverse currents and the density of states. The influence on these properties of the structural disorder is analyzed by comparing the results for one-component crystals with those for liquids and supercooled liquids at analogous conditions. The effects of species-disorder on the collective properties of binary crystals are also discussed.

Electronic structure and properties of Cu2O

The structural and electronic properties of Cu2O have been investigated using the periodic Hartree-Fock method and a posteriori density-functional corrections. The lattice parameter, bulk modulus, and elastic constants have been calculated. The electronic structure of and bonding in Cu2O are analyzed and compared with x-ray photoelectron spectroscopy spectra, showing a good agreement for the valence-band states. To check the quality of the calculated electron density, static structure factors and Compton profiles have been calculated, showing a good agreement with the available experimental data. The effective electron and hole masses have been evaluated for Cu2O at the center of the Brillouin zone. The calculated interaction energy between the two interpenetrated frameworks in the cuprite structure is estimated to be around -6.0 kcal/mol per Cu2O formula. The bonding between the two independent frameworks has been analyzed using a bimolecular model and the results indicate an important role of d10-d10 type interactions between copper atoms.

Magnetic properties of Fe-Cu-Nb-Si-B nanocrystaliine magnetic alloys

Several ribbons of composition Fe73.5Cu1Nb 3Si16.5B6 and Fe73.5Cu1 Nb3Si13.5B9 were prepared by annealing the as-quenched samples between 525°C and 700°C; which induced nucleation of nanocrystallites of Fe bcc-type composition. Mean grain sizes were obtained from X-ray diffraction. Static magnetic properties were measured with both a Magnet Physik Hysteresis-Graph (up to 200 Oe) and a SHE SQUID magnetometer (up to 50 kOe). Soft magnetic parameters (coercive field and initial permeability) were very sensitive to grain size. The ZFC magnetization at low field showed a broad peak at a temperature TM, thus signalling a certain distribution of nanocrystalline sizes, and TM strongly decreased when the mean grain size decreased. Isothermal magnetization curves at low temperature showed the expected asymptotic behavior of a random magnet material at low and high fields.

General method to determine replica symmetry breaking transitions

We introduce a new parameter to investigate replica symmetry breaking transitions using finite-size scaling methods. Based on exact equalities initially derived by F. Guerra this parameter is a direct check of the self-averaging character of the spin-glass order parameter. This new parameter can be used to study models with time reversal symmetry but its greatest interest lies in models where this symmetry is absent. We apply the method to long-range and short-range Ising spin-glasses with and without a magnetic field as well as short-range multispin interaction spin-glasses.

Self-similarity properties of natural images resemble those of turbulent flows

We show that the statistics of an edge type variable in natural images exhibits self-similarity properties which resemble those of local energy dissipation in turbulent flows. Our results show that self-similarity and extended self-similarity hold remarkably for the statistics of the local edge variance, and that the very same models can be used to predict all of the associated exponents. These results suggest using natural images as a laboratory for testing more elaborate scaling models of interest for the statistical description of turbulent flows. The properties we have exhibited are relevant for the modeling of the early visual system: They should be included in models designed for the prediction of receptive fields.

Generalized Onsager symmetry

Onsager's symmetry theorem for transport near equilibrium is extended in two directions. A corresponding symmetry is obtained for linear transport near nonequilibrium stationary states, and the class of transport laws is extended to include nonlocality in both space and time. The results are formally exact and independent of any specific model for the nonequilibrium state.

Asymmetric reversal in inhomogeneous magnetic heterostructures

Asymmetric magnetization reversal is an unusual phenomenon in antiferromagnet/ferromagnet (AF/FM) exchange biased bilayers. We investigated this phenomenon in a simple model system experimentally and by simulation assuming inhomogeneously distributed interfacial AF moments. The results suggest that the observed asymmetry originates from the intrinsic broken symmetry of the system, which results in local incomplete domain walls parallel to the interface in reversal to negative saturation of the FM. The magneto-optical Kerr effect unambiguously confirms such an asymmetric reversal and a depth-dependent FM domain wall in accord with the magnetometry and simulations.

Clustering in complex networks. II. Percolation properties

The percolation properties of clustered networks are analyzed in detail. In the case of weak clustering, we present an analytical approach that allows us to find the critical threshold and the size of the giant component. Numerical simulations confirm the accuracy of our results. In more general terms, we show that weak clustering hinders the onset of the giant component whereas strong clustering favors its appearance. This is a direct consequence of the differences in the k-core structure of the networks, which are found to be totally different depending on the level of clustering. An empirical analysis of a real social network confirms our predictions.

Properties of resonant activation phenomena

The phenomenon of resonant activation of a Brownian particle over a fluctuating barrier is revisited. We discuss the important distinctions between barriers that can fluctuate among up and down configurations, and barriers that are always up but that can fluctuate among different heights. A resonance as a function of the barrier fluctuation rate is found in both cases, but the nature and physical description of these resonances is quite distinct. The nature of the resonances, the physical basis for the resonant behavior, and the importance of boundary conditions are discussed in some detail. We obtain analytic expressions for the escape time over the barrier that explicitly capture the minima as a function of the barrier fluctuation rate, and show that our analytic results are in excellent agreement with numerical results.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models