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Critical percolation phase and thermal Berezinskii-Kosterlitz-Thouless transition in a scale-free network with short-range and long-range random bonds

Berker, A. Nihat and Hinczewski, Michael and Netz, Roland R. (2009) Critical percolation phase and thermal Berezinskii-Kosterlitz-Thouless transition in a scale-free network with short-range and long-range random bonds. Physical Review E, 80 (4). 041118. ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.80.041118

Abstract

Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic (Berezinskii-Kosterlitz-Thouless) geometric order, occurs in the phase diagram, in addition to the ordinary (compact) percolating phase and the non-percolating phase. It is found that no connection exists between, on the one hand, the onset of this geometric BKT behavior and, on the other hand, the onsets of the highly clustered small-world character of the network and of the thermal BKT transition of the Ising model on this network. Nevertheless, both geometric and thermal BKT behaviors have inverted characters, occurring where disorder is expected, namely at low bond probability and high temperature, respectively. This may be a general property of long-range networks.

Item Type:Article
Uncontrolled Keywords:Scale-free networks, small-world networks, hierarchical lattices, geometrical correlations, thermal correlations, percolation, phase transitions, renormalization-group theory
Subjects:Q Science > QC Physics > QC310.15 Thermodynamics
Q Science > QC Physics > QC176-176.9 Solids. Solid state physics
ID Code:13424
Deposited By:A. Nihat Berker
Deposited On:05 Dec 2009 20:06
Last Modified:25 May 2011 14:07

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