We have studied diffusion-limited reaction on a one-dimensional lattice under the quenched disorder using Monte Carlo simulations. The hopping probabilities at a site is distributed by the power law p(y)=νyν−1 with 0<ν⩽1 and 0<y⩽1. The density of the reactants decays according to a power law, C(t)∼t−α(ν) for A+A→0 and A+B→0 annihilation reaction. The exponent α(ν) depends on the disorder exponent ν. For A+A→0, we have found α(ν)=ν/(1+ν). For A+B→0, we have observed α=0.25 at ν>0.4 and α decreases monotonically for α<0.4.

We investigate the critical behavior of a model that mimics the propagation of an epidemic process over a population mediated by a density of diffusive individuals which can infect a static population upon contact. We simulate the above model on finite chains to determine the critical density of...

The mA + nB → Ø diffusion limited reaction with homogeneous initial condition is studied analytically and numerically. Through renormalization group arguments, it is shiown that the system exhibits the anomalous kinetic behavior below the critical dimension dc∗ ≡ 4/(m + n − 1)....

We investigate, using mean-field theory and simulation, the effect of asymmetry on the critical behavior and probability density of Bak–Sneppen models. Two kinds of anisotropy are investigated: (i) different numbers of sites to the left and right of the central (minimum) site are updated and...

In this work we study an unusual phase transition of the Baxter–Wu model in the presence of an external magnetic field. The model is pure Baxter–Wu, which means that only three-spin interactions are taken into account. We construct a phase diagram on the temperature–field plane based...

Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an inhomogeneous active region, coupled and uncoupled, respectively....

We investigate the short-time critical dynamics of the Baxter–Wu (BW) and n=3 Turban (3TU) models to estimate their global persistence exponent θg. We conclude that this new dynamical exponent can be useful in detecting differences between the critical behavior of these models which are very...

We study the distribution of number of neighbors, ζ, of a multifractal self-affine lattice, Qmf, defined by a single parameter ρ. ζ is neither a constant like in regular lattices nor follows a Gaussian distribution as in the Voronoi lattice. The histogram of ζ show exponential behavior for...

Using multiscaling analysis of the recent data on the X-ray solar flares obtained by the satellite observatory (The Reuven Ramaty High-Energy Solar Spectroscopic Imager,) (NASA), it is shown that the flares phenomenon belongs to the “critical fragmentation” class of universality (Phys. Rev....

We show how size-contingent laws can be used to identify the equilibrium and welfare effects of labor regulation. Our framework incorporates such regulations into the Lucas (1978) model and applies this to France where many labor laws start to bind on firms with exactly 50 or more employees....