Complex systems may show strongly non-exponential relaxation, the origins of these behavior seem to be related to the fractal structure of the phase space. In this article, we consider the diffusion on a dilute hypercube, this stochastic process is a coarse-grained model for the time evolution...

We individuated a method to distinguish a glass phase from a highly viscous liquid phase in a lattice of vortices, established in type-two superconductors. Our analysis is based on the study of the temperature dependence of numerically obtained 1st and 3rd harmonics curves of the AC magnetic...

We analyze the validity of the fluctuation–dissipation theorem for slow relaxation systems in the context of mesoscopic nonequilibrium thermodynamics. We demonstrate that the violation arises as a natural consequence of the elimination of fast variables in the description of a glassy system,...

We review the results of a statistical mechanics approach to granular materials and its extension to non-thermal systems in their “inherent states”. We introduce a “tapping” dynamics, based on a dynamics used for real granular matter, which allows to visit the space of the inherent...

We show the existence of intermittent dynamics in one of the simplest model of a glassy system: the two-state model, which has been used [Physica A 329 (2003) 357] to explain the origin of the violation of the fluctuation–dissipation theorem. The dynamics is analyzed through a Langevin...

We study the phase diagram of glassy systems in the presence of an attractive coupling among real replicas. We find competition among a localized and a delocalized phase, that are separated by a coexistence line as in ordinary first-order phase transitions. The coexistence line terminates in a...

Conformal field theory (CFT) predicts universal relations between scaling amplitudes and scaling dimensions for two-dimensional systems on infinite length cylinders, which hold true even independent of the model under consideration. We discuss different possible generalizations of such laws to...

We introduce aperiodic, but deterministic, dilution of bonds in the Ising model with competing ferro and antiferromagnetic interactions between first and second neighbors along the branches of a Cayley tree. The problem is formulated as a non-linear dissipative map, whose attractors correspond...

The paper discusses the transformation of decorated Ising models into an effective undecorated spin model, using the most general Hamiltonian for interacting Ising models including a long range and high order interactions. The inverse of a Vandermonde matrix with equidistant nodes [−s,s] is...

Through Monte Carlo Simulation, the well-known majority-vote model has been studied with noise on directed random graphs. In order to characterize completely the observed order–disorder phase transition, the critical noise parameter qc, as well as the critical exponents β/ν, γ/ν and 1/ν...