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...

The height–height correlations of the surface growth for equilibrium and nonequilibrium restricted solid-on-solid (RSOS) model were investigated on randomly diluted lattices, i.e., on infinite percolation networks. It was found that the correlation function calculated over the chemical...

We investigate the critical behavior of nonequilibrium phase transition from an active phase to an absorbing state on two selected fractal lattices, i.e., on a checkerboard fractal and on a Sierpinski carpet. The checkerboard fractal is finitely ramified with many dead ends, while the...

A one-step real-space renormalization group (RSRG) transformation is used to study the q-state Potts model on the two-dimensional (2D) Penrose tiling (PT). The critical exponents of the correlation length ν(q) in the region between q=1 and q=4 are obtained. The bond percolation (BP) threshold...

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated...