The effectiveness of the perturbative renormalization group approach at fixed space dimension d in the theory of critical phenomena is analyzed. Three models are considered: the O(N) model, the cubic model and the ...

We study the purely relaxational critical dynamics with non-conserved order parameter (model A critical dynamics) for three-dimensional magnets with disorder in a form of the random anisotropy axis. For the random ...

We review recent results of the field theoretical renormalization group analysis on the scaling properties of star polymers. We give a brief account of how the numerical values of the exponents governing the scaling of ...

We make a short overview of the recent analytic and numerical studies of the classical two-dimensional XY and Heisenberg models at low temperatures. Special attention is being paid to an influence of finite system size L ...

We performed a series of simulations for a linear polymer chain in a solvent using dissipative particle dynamics to check the scaling relations for the end-to-end distance, radius of gyration and hydrodynamic radius in ...

In these lectures I discuss peculiarities of the critical behaviour of “non-ideal” systems as it is explained by the renormalization group approach. Examples considered here include account of the single-ion anisotropy, ...

We discuss the photograph procured from the archives of the V.Stefanyk Lviv National Scientific Library of Ukraine dated by 1904 which shows Marian Smoluchowski together with professors and graduate students of the Philosophy ...

The effect of a local anisotropy of random orientation on a ferromagnetic phase transition is studied. To this end, a model of a random anisotropy magnet is analysed by means of a field theoretical renormalization ...

We consider the Ising model on an annealed scale-free network with node-degree distribution characterized by a power-law decay P(K)∼ K-λ. It is well established that the model is characterized by classical mean-field ...