Critical percolation phase and thermal Berezinskii-Kosterlitz-Thouless transition in a scale-free network with short-range and long-range random bonds
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Berker-2009-Critical Percolation phase and thermal.pdf
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Author(s)
Berker, A. Nihat
Hinczewski, Michael
Netz, Roland R.
Date Issued
October 2009
Journal
Physical Review E
Publisher
American Physical Society
Citation
Berker, A. Nihat, Michael Hinczewski, and Roland R. Netz. “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 (2009): 041118.© 2009 The American Physical Society
Version
Final published version
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 (BKT)] geometric order, occurs in the phase diagram in addition to the ordinary (compact) percolating phase and the nonpercolating 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
http://dx.doi.org/10.1103/PhysRevE.80.041118
