No abstract

We analyze the nonequilibrium athermal random field Ising model (RFIM) at equilateral cubic lattices of finite size L and show that the entire range of disorder consists of three distinct domains in which the model manifests different scaling behaviour. The first domain contains the values of disorder R that are below the critical disorder R c where the spanning avalanches almost surely appear when the system is driven by the external magnetic field. The spanning avalanches become unlikely for disorders above the size-dependent effective disorder R c eff ( L ) > R c , and the system response is size-independent. Between the foregoing two lies the domain of transitional disorders

No abstract

No abstract

We study the statistics of lattice animals on a class of hierarchical graphs whose members can be labeled by a set of integers , g≥1. We have shown that the animal critical behavior crucially depends on the minimal value of these parameters. For we find the usual power-law behavior, while for the associated generating function displays an essential singularity ∼exp[c(tc−t)−ψ], where c is a constant and the exponent ψ is related to the leading correction term in the asymptotic behavior of the number of animal configurations having N bonds, , ω = ψ/(ψ+1). We express the entropic exponent ω and the animal size exponent in terms of pertinent graph parameters.