159 research outputs found
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
Finite size induced phenomena in 2D classical spin models
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 on the
peculiarities of the low-temperature phase. In accordance with the
Mermin-Wagner-Hohenberg theorem, spontaneous magnetisation does not appear in
the above models at infinite L. However it emerges for the finite system sizes
and leads to new features of the low-temperature behaviour.Comment: 4 pages, submitted to the proceedings of the 2nd International
Conference on Quantum Electrodynamics and Statistical Physics (Kharkiv,
Ukraine, 19-23 September, 2006
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 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
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