Absence of self-organized criticality in a random-neighbor version of the OFC stick-slip model

We report some numerical simulations to investigate the existence of a self-organized critical (SOC) state in a random-neighbor version of the OFC model for a range of parameters corresponding to a non-conservative case. In contrast to a recent work, we do not find any evidence of SOC. We use a more realistic distribution of energy among sites to perform some analytical calculations that agree with our numerical conclusions.Comment: 7 pages, 4 figures, submitted to Physica

Universal Critical Behavior of Aperiodic Ferromagnetic Models

We investigate the effects of geometric fluctuations, associated with aperiodic exchange interactions, on the critical behavior of $q$-state ferromagnetic Potts models on generalized diamond hierarchical lattices. For layered exchange interactions according to some two-letter substitutional sequences, and irrelevant geometric fluctuations, the exact recursion relations in parameter space display a non-trivial diagonal fixed point that governs the universal critical behavior. For relevant fluctuations, this fixed point becomes fully unstable, and we show the apperance of a two-cycle which is associated with a novel critical behavior. We use scaling arguments to calculate the critical exponent $\alpha$ of the specific heat, which turns out to be different from the value for the uniform case. We check the scaling predictions by a direct numerical analysis of the singularity of the thermodynamic free-energy. The agreement between scaling and direct calculations is excellent for stronger singularities (large values of $q$). The critical exponents do not depend on the strengths of the exchange interactions.Comment: 4 pages, 1 figure (included), RevTeX, submitted to Phys. Rev. E as a Rapid Communicatio

Simulation study of the inhomogeneous Olami-Feder-Christensen model of earthquakes

Statistical properties of the inhomogeneous version of the Olami-Feder-Christensen (OFC) model of earthquakes is investigated by numerical simulations. The spatial inhomogeneity is assumed to be dynamical. Critical features found in the original homogeneous OFC model, e.g., the Gutenberg-Richter law and the Omori law are often weakened or suppressed in the presence of inhomogeneity, whereas the characteristic features found in the original homogeneous OFC model, e.g., the near-periodic recurrence of large events and the asperity-like phenomena persist.Comment: Shortened from the first version. To appear in European Physical Journal