%0 Book Section %1 statphys23_1030 %A Dorogovtsev, S.N. %A Goltsev, A.V. %A Khajeh, E. %A Mendes, J.F.F. %A Oliveira, J.G. %A Samukhin, A.N. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K complex correlations critical networks phenomena statphys23 topic-11 %T Critical phenomena and finite-size effects in growing networks %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1030 %X 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).

@incollection{statphys23_1030, 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).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Dorogovtsev, S.N. and Goltsev, A.V. and Khajeh, E. and Mendes, J.F.F. and Oliveira, J.G. and Samukhin, A.N.}, biburl = {https://www.bibsonomy.org/bibtex/21e3d086bc130b096051bad16747799a2/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {e9751e409da209e7b4250b2e58624fb8}, intrahash = {1e3d086bc130b096051bad16747799a2}, keywords = {complex correlations critical networks phenomena statphys23 topic-11}, month = {9-13 July}, timestamp = {2007-06-20T10:16:37.000+0200}, title = {Critical phenomena and finite-size effects in growing networks}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1030}, year = 2007 }