The field theory renormalization group is used for analyzing the fractional Langevin equation with the order of the temporal derivative 0α1, fractional Laplacian of the order σ, and Gaussian noise correlator. The case of non-linearity φm with odd m≥3 is considered. It is proved that the...

Nonlinear effects in the two-component medium with conductivities σ1 (metal) and σ2 (insulator) near the percolations threshold is studied. For the medium having cubic nonlinearity an effective nonlinear conductivity ae and correlation functions of the electrical field 〈e4〉 and current...

The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D ferromagnetic Ising model on 3D Voronoi–Delauney lattices. It is assumed that the coupling factor J varies with the distance r between the first neighbors as J(r)∝e−ar, with a≥0. The...

The rigorous explanation for the term |t|2β in the rectilinear diameter equation is given (t=(Tc−T)/Tc, β is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric, is constructed within the...

In the frameworks of the geometrical approach developed earlier, the situation is considered when in the branch point of the zero-field curve the first non-vanishing derivatives of the Gibbs potential w.r.t., the order parameters are of the sixth order, and w.r.t. the “critical” correlation...

The six-dimensional Ising model is simulated on the Creutz cellular automaton using the finite-size lattices with the linear dimension 4⩽L⩽10. The exponents in the finite-size scaling relations for the magnetic susceptibility and the order parameter at the infinite-lattice critical...

Random walk simulations based on a molecular trajectory algorithm are performed on critical percolation clusters. The analysis of corrections to scaling is carried out. It has been found that the fractal dimension of the random walk on the incipient infinite cluster is dw=2.873±0.008 in two...

We use the optimized perturbation theory, or linear δ expansion, to evaluate the critical exponents in the critical 3d O(N) invariant scalar field model. Regarding the implementation procedure, this is the first successful attempt to use the method in this type of evaluation. We present and...

We introduce a model for the Contact Process with relaxing immunization CPRI. In this model, local memory is introduced by a time and space dependence of the contamination probability. The model has two parameters: a typical immunization time τ and a maximum contamination probability a. The...

An inverted rank distribution is an infinite sequence of positive sizes ordered in a monotone increasing fashion. Interlacing together Lorenzian and oligarchic asymptotic analyses, we establish a macroscopic classification of inverted rank distributions into five “socioeconomic” universality...