Introduction to renormalization

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, structural disorder, frustrations. I introduce main ideas of renormalization and show how it serves the explanation of typical features of criticality in the above systems: softening of the phase transition, changes in the universality class, complicated effective critical behaviour.Comment: Lecture given at the Mochima spring school on foundations of statistical and mesoscopic physics, Mochima, Venezuela, June 200

Towards journalometrical analysis of a scientific periodical: a case study

In this paper we use several approaches to analyse a scientific journal as a complex system and to make a possibly more complete description of its current state and evolution. Methods of complex networks theory, statistics, and queueing theory are used in this study. As a subject of the analysis we have chosen the journal ``Condensed Matter Physics'' (http://www.icmp.lviv.ua/journal/). In particular, based on the statistical data regarding the papers published in this journal since its foundation in 1993 up to now we have composed the co-authorship network and extracted its main quantitative characteristics. Further, we analyse the priorities of scientific trends reflected in the journal and its impact on the publications in other editions (the citation ratings). Moreover, to characterize an efficiency of the paper processing, we study the time dynamics of editorial processing in terms of queueing theory and human activity analysis

Fractal transit networks: self-avoiding walks and L\'evy flights

Using data on the Berlin public transport network, the present study extends previous observations of fractality within public transport routes by showing that also the distribution of inter-station distances along routes displays non-trivial power law behaviour. This indicates that the routes may in part also be described as L\'evy-flights. The latter property may result from the fact that the routes are planned to adapt to fluctuating demand densities throughout the served area. We also relate this to optimization properties of L\'evy flights.Comment: 7 pages, 3 figures, style files included. Submitted to the topical issue 'From Brownian motion to self-avoiding walks and L\'evy flights' of the journal 'EPJ - Special Topics

Phase Transition in the Random Anisotropy Model

The influence of a local anisotropy of random orientation on a ferromagnetic phase transition is studied for two cases of anisotropy axis distribution. To this end a model of a random anisotropy magnet is analyzed by means of the field theoretical renormalization group approach in two loop approximation refined by a resummation of the asymptotic series. The one-loop result of Aharony indicating the absence of a second-order phase transition for an isotropic distribution of random anisotropy axis at space dimension $d<4$ is corroborated. For a cubic distribution the accessible stable fixed point leads to disordered Ising-like critical exponents.Comment: 10 pages, 2 latex figures and a style file include

Biconical critical dynamics

A complete two loop renormalization group calculation of the multicritical dynamics at a tetracritical or bicritical point in anisotropic antiferromagnets in an external magnetic field is performed. Although strong scaling for the two order parameters (OPs) perpendicular and parallel to the field is restored as found earlier, in the experimentally accessible region the effective dynamical exponents for the relaxation of the OPs remain different since their equal asymptotic values are not reached.Comment: 6 pages, 2 figures; some additions, corrected typo