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Vendredi 4 Novembre 2011 - Y. Holovathch - Critical behaviour in complex networks : scaling and beyond

par LABGPM - publié le

Vendredi 4 Novembre 2011 - 10h30

Critical behaviour in complex networks : scaling and beyond

Phase transitions and critical behavior in complex networks currently attract much attention because of their unusual features and broad array of applications, ranging from socio- to nanophysics. The questions we address in this report concern two fundamental principles of critical phenomena : universality and scaling. Both of these questions have to be reconsidered when a system resides on a network. To this end, we consider several simple models on scale-free networks and analyze their critical behavior in terms of scaling functions which are of fundamental interest in the theory of critical phenomena. We obtain general scaling functions for the equations of state and thermodynamical functions extending the principle of universality to systems on scale-free networks and quantifying an impact of fluctuations in the network structure on critical behavior. Moreover, we address the logarithmic corrections to the leading power laws governing thermodynamic quantities that appear as the second order phase transition point is approached. We show the validity of scaling relations for the new set of the logarithmic correction-to-scaling exponents and derive new scaling relations for the exponents of logarithmic corrections, for which these relations were unknown.

1. C. von Ferber, R. Folk, Yu. Holovatch, R. Kenna, V. Palchykov.
Phys. Rev. E 83 (2011) 061114

2. V. Palchykov, C. von Ferber, R. Folk, Yu. Holovatch, R. Kenna.
Phys. Rev. E 82 (2010) 011145.