The critical behaviour of thin films containing quenched random impurities and inhomogeneities is investigated by the renormalization-group method to the one-loop order within the framework of the n-component φ4-model. The finite-size crossover in impure films has been considered on the basis...

We study the annihilation reaction A+A→0 in a two-dimensional square lattice of width W and an infinite length. The behaviour of the density of particles ρ(t) is analyzed. This system exhibits a crossover time tc between the short-time (two-dimensional) and the long-time (one-dimensional)...

We propose a two-dimensional continuum percolation model in an anisotropic medium, which consists of parallel chains of sites coupled to each other weakly via rare “impurities”. By checking simultaneously two percolations, parallel and perpendicular to the chain direction, we show that while...