@incollection{statphys23_1030,
	title = {Critical phenomena and finite-size effects in growing networks},
	address = {Genova, Italy},
	author = {S.N. Dorogovtsev and A.V. Goltsev and E. Khajeh and J.F.F. Mendes and J.G. Oliveira and A.N. Samukhin},
	booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
	editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
	month = {9-13 July},
	url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1030},
	year = {2007},
	biburl = {http://www.bibsonomy.org/bibtex/21e3d086bc130b096051bad16747799a2/statphys23},
	abstract = {We review known critical effects in various cooperative models on growing networks, as well as structural transitions in these networks, and present a unified approach to these phenomena. Also, we discuss finite-size scaling in networks in the framework of a general phenomenological theory and describe basic finite-size effects. 

We demonstrate and explain the universality of the critical phenomena in random recursive graphs, some deterministic networks, and a more general class of evolving networks. We explain the nature of the Berezinskii-Kosterlitz-Thouless-like singularities which frequently occur in these networks. By using the example of the $(q>2)$-state Potts model, we demonstrate the transformation of even a first order phase transition to infinite order transition. 

Finally, we give a unified description of the correlations in cooperative models  on complex networks. We present our new results on the critical statistics of the correlation volume in networks and apply them to a number of basic models.  


[1] S. N. Dorogovtsev, A. V. Goltsev, and J.F.F. Mendes, ``Critical phenomena in  complex networks'', to be published. 

[2] S.N. Dorogovtsev, A.V. Goltsev, and J.F.F. Mendes, ``Correlations in interacting systems with a network topology'', Phys. Rev. E 72, 066130 (2005). 

[3] E. Khajeh, S. N. Dorogovtsev, and J. F. F. Mendes, ``BKT-like transition in   the Potts model on an inhomogeneous annealed network'', cond-mat/0701156. 

[4] S. N. Dorogovtsev, A. V. Goltsev, and  J. F. F. Mendes, ``$k$-core organization of complex networks'', Phys. Rev. Lett. 96, 040601 (2006). 

[5] S. N. Dorogovtsev and  J. F. F. Mendes, ``Evolution of Networks: From Biological Nets to the Internet and WWW'' (Oxford University Press, Oxford, 2003); Adv. Phys. 51, 1079 (2002). 

[6] S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, ``Anomalous percolation properties of growing networks'', Phys. Rev. E 64, 066110 (2001). 

[7] A. V. Goltsev, S. N. Dorogovtsev, and J. F. F. Mendes, ``$k$-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects'', Phys. Rev. E 73, 056101 (2006).},
	keywords = {complex correlations critical networks phenomena statphys23 topic-11 }
}