The K-sat problem in a simple limit

We compute the thermodynamic properties of the 3-satisfiability problem in the infinite connectivity limit. In this limit the computations can be strongly simplified and the thermodynamical properties can be obtained with an high accuracy. We find evidence for a continuous replica symmetry breaking in the region of high number of clauses, $\alpha > \alpha_c$.Comment: 9 pages, 6 figures. To appear in J. Stat. Phys. Minor change

Stable Solution of the Simplest Spin Model for Inverse Freezing

We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction that displays the inverse freezing phenomenon. The behavior of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and spinodal lines for the model are computed using the Full Replica Symmetry Breaking Ansatz that always yields a thermodynamically stable phase. We compare the results both with the formulation of the same model in terms of Ising spins on lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. {\bf 93} 037202 (2004)], for which the reentrance is enhanced as the ratio between the degeneracy of full to empty sites increases. The simplest version of all these models, known as the Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase, including the right thermodynamic behavior.Comment: 4 pages, 4 figure

Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation

A careful critical analysis of the complexity, at the annealed level, of the Sherrington-Kirkpatrick model has been performed. The complexity functional is proved to be always invariant under the Becchi-Rouet-Stora-Tyutin supersymmetry, disregarding the formulation used to define it. We consider two different saddle points of such functional, one satisfying the supersymmetry [A. Cavagna {\it et al.}, J. Phys. A {\bf 36} (2003) 1175] and the other one breaking it [A.J. Bray and M.A. Moore, J. Phys. C {\bf 13} (1980) L469]. We review the previews studies on the subject, linking different perspectives and pointing out some inadequacies and even inconsistencies in both solutions.Comment: 20 pages, 4 figure

Neural-Based Nonlinear Device Models for Intermodulation Analysis

A new procedure to learn a nonlinear model together with its derivative parameters using a composite neural network is presented.So far neural networks have never been used to extract large-signal device model accounting for distortion parameters.Applying this method to FET devices leads to nonlinear models for current- voltage functions which allow improved prediction of weak and mildly device nonlinearities in the whole bias region. The resulting models have demonstrated to be suitable for both small-signal and large-signal analyses,including intermodulation distortion prediction

The random Blume-Capel model on cubic lattice: first order inverse freezing in a 3D spin-glass system

We present a numerical study of the Blume-Capel model with quenched disorder in 3D. The phase diagram is characterized by spin-glass/paramagnet phase transitions of both first and second order in the thermodynamic sense. Numerical simulations are performed using the Exchange-Monte Carlo algorithm, providing clear evidence for inverse freezing. The main features at criticality and in the phase coexistence region are investigated. The whole inverse freezing transition appears to be first order. The second order transition appears to be in the same universality class of the Edwards-Anderson model. The nature of the spin-glass phase is analyzed by means of the finite size scaling behavior of the overlap distribution functions and the four-spins real-space correlation functions. Evidence for a replica symmetry breaking-like organization of states is provided.Comment: 18 pages, 24 figures, 7 table

Breeze analysis by mast and sodar measurements

During the year 1993, field measurements were carried out in a meteorological station located in the neighbourhood of Rome, 10 km from the coast (Tyrrhenian Sea). The monitoring station is composed of a 30 m mast and a three-axial Doppler sodar. A statistical analysis of data has been made in order to obtain the main parameters utilised by the dispersion model. Hourly, seasonal and conditional averages showed the strong influence of sea and land breeze circulation on the local characteristics of the atmospheric boundary layer. Such an aspect has to be considered in the numerical predictions of pollutant dispersion

Diluted one-dimensional spin glasses with power law decaying interactions

We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models. The spin-glass phase is studied in and out of the range of validity of the mean-field approximation in order to discriminate between different theories. Since each variable interacts only with a finite number of others the cost for simulating the model is drastically reduced with respect to the fully connected version and larger sizes can be studied. We find both static and dynamic evidence in favor of the so-called replica symmetry breaking theory.Comment: 4 pages, 6 figures, 2 table

Phase diagram and complexity of mode-locked lasers: from order to disorder

We investigate mode-locking processes in lasers displaying a variable degree of structural randomness, from standard optical cavities to multiple-scattering media. By employing methods mutuated from spin-glass theory, we analyze the mean-field Hamiltonian and derive a phase-diagram in terms of the pumping rate and the degree of disorder. Three phases are found: i) paramagnetic, corresponding to a noisy continuous wave emission, ii) ferromagnetic, that describes the standard passive mode-locking, and iii) the spin-glass in which the phases of the electromagnetic field are frozen in a exponentially large number of configurations. The way the mode-locking threshold is affected by the amount of disorder is quantified. The results are also relevant for other physical systems displaying a random Hamiltonian, like Bose-Einstein condensates and nonlinear optical beams.Comment: 4 pages, 2 figure

The Ising M-p-spin mean-field model for the structural glass: continuous vs. discontinuous transition

The critical behavior of a family of fully connected mean-field models with quenched disorder, the $M-p$ Ising spin glass, is analyzed, displaying a crossover between a continuous and a random first order phase transition as a control parameter is tuned. Due to its microscopic properties the model is straightforwardly extendable to finite dimensions in any geometry.Comment: 10 pages, 1 figure, 1 tabl

Ising spin glass transition in magnetic field out of mean-field

The spin-glass transition in external magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Evidence for a spin-glass transition in magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field.Comment: 5 pages, 1 table, 6 figures, data analysis mistake corrected, new figures, new scaling approach to critical properties introduce