A procedure for deriving general nonlinear Fokker–Planck equations (FPEs) directly from the master equation is presented. The nonlinear effects are introduced in the transition probabilities, which present a dependence on the probabilities for finding the system in a given state. It is shown...

The experimental formation factor (F) vs. porosity (φ) as well as resistivity index (I) vs. water saturation (Sw) results typically present, in double-logarithmic representation, bendings which we now interpret as crossovers between different fractal-like regimes. We consistently propose for...

A spin-glass model, with two Ising coupled systems (real replicas), is investigated in the limit of infinite-range interactions, through the replica method. Besides the Ising representation, the model is also considered as a discrete two-component four-state clock spin glass. The phase diagram...

Ising spin glasses are studied, at zero temperature, on a hierarchical lattice as an approach to the square lattice. The stiffness exponent y, which governs the behavior of the interactions under changes of scale, is computed for several distinct continuous symmetric probability distributions...

A system of N classical Heisenberg-like rotators, characterized by infinite-range ferromagnetic interactions, is studied numerically within the microcanonical ensemble through a molecular-dynamics approach. Such a model, known as the classical inertial infinite-range-interaction Heisenberg...

The ±J Ising spin glass [probabilities p and (1−p) associated with ferromagnetic and antiferromagnetic couplings, respectively] is studied, at zero temperature, on a hierarchical lattice that approaches the square lattice. It is shown that, for a wide range of values of p [between (1−pc)...

The (Nα,Nβ) model is investigated within the damage-spreading framework. Exact relations involving thermodynamic quantities (order parameters and correlation functions) and conveniently defined combinations of damages are obtained, which are valid for any regular (translationally invariant)...

The evolution of the Hamming distance (damage) for the fully frustrated Ising model on the square lattice is analyzed numerically within both Glauber and heat-bath dynamic frameworks. The chaotic regime, for which an infinitesimal initial perturbation propagates, is found at all temperatures in...

We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired...