Yu. Holovatch

Public transport networks: empirical analysis and modeling

Public transport networks of fourteen cities of so far unexplored network size are analyzed in standardized graph representations: the simple graph of the network map, the bipartite graph of routes and stations, and both one mode projections of the latter. Special attention is paid to the inter-relations and spatial embedding of transport routes. This systematic approach reveals rich behavior beyond that of the ubiquitous scale-free complex network. We find strong evidence for structures in PTNs that are counter-intuitive and need to be explained, among these a pronounced diversity in the expression of typical network characteristics within the present sample of cities, a surprising geometrical behavior with respect to the two-dimensional geographical embedding and an unexpected attraction between transport routes. A simple model based on these observations reproduces many of the identified PTN properties by growing networks of attractive self-avoiding walks.

Network harness: Metropolis public transport

We analyze the public transport networks (PTNs) of 14 major cities of the world. While the primary network topology is defined by a set of routes each servicing an ordered series of given stations, a number of different neighborhood relations may be defined both for the routes and the stations. The networks defined in this way display distinguishing properties, the most striking being that often several routes proceed in parallel for a sequence of stations. Other networks with real-world links like cables or neurons embedded in two or three dimensions often show the same feature—we use the car engineering term harness for such networks. Geographical data for the routes reveal surprising self-avoiding walk (SAW) properties. We propose and simulate an evolutionary model of PTNs based on effectively interacting SAWs that reproduces the key features.

Criticality of the random-site Ising model: Metropolis, Swendsen-Wang and Wolff Monte Carlo algorithms

D. Ivaneyko, J. Ilnytskyi, B. Berche, Yu. Holovatch 1 Ivan Franko National University of Lviv, 79005 Lviv, Ukraine 2 Institute for Condensed Matter Physics, National Acad. Sci. of Ukraine, 79011 Lviv, Ukraine 3 Laboratoire de Physique des Materiaux, Universite Henri Poincare 1, 54506 Vandœuvre les Nancy Cedex, France 4 Institut fur Theoretische Physik, Johannes Kepler Universitat Linz, 4040 Linz, Austria

Critical dynamics and effective exponents of magnets with extended impurities

We investigate the asymptotic and effective static and dynamic critical behavior of (d=3)-dimensional magnets with quenched extended defects, correlated in

Violation of Lee-Yang circle theorem for Ising phase transitions on complex networks

epsilon_d

Universal features of polymer shapes in crowded environments

dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining

Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble

d-epsilon_d

Critical phenomena on scale-free networks: Logarithmic corrections and scaling functions

dimensions. The field-theoretical renormalization group perturbative expansions being evaluated naively do not allow for the reliable numerical data. We apply the Chisholm-Borel resummation technique to restore convergence of the two-loop expansions and report the numerical values of the asymptotic critical exponents for the model A dynamics. We discuss different scenarios for static and dynamic effective critical behavior and give values for corresponding non-universal exponents.

Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

The Ising model on annealed complex networks with degree distribution decaying algebraically as

Field theory of bicritical and tetracritical points. I. Statics

p(K)sim K^{-lambda}