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Critical phenomena on scale-free networks: logarithmic corrections and scaling functions | | V. Palchykov
; C. von Ferber
; R. Folk
; Yu. Holovatch
; R. Kenna
; | | Date: |
1 Apr 2010 | | Abstract: | In this paper, we address the logarithmic corrections to the leading power
laws that govern thermodynamic quantities as a second-order phase transition
point is approached. For phase transitions of spin systems on d-dimensional
lattices, such corrections appear at some marginal values of the order
parameter or space dimension. We present new scaling relations for these
exponents. We also consider a spin system on a scale-free network which
exhibits logarithmic corrections due to the specific network properties. To
this end, we analyze the phase behavior of a model with coupled order
parameters on a scale-free network and extract leading and logarithmic
correction-to-scaling exponents that determine its field- and temperature
behavior. Although both non-trivial sets of exponents emerge from the
correlations in the network structure rather than from the spin fluctuations
they fulfil the respective thermodynamic scaling relations. For the scale-free
networks the logarithmic corrections appear at marginal values of the node
degree distribution exponent. In addition we calculate scaling functions, which
also exhibit nontrivial dependence on intrinsic network properties. | | Source: | arXiv, 1004.0097 | | Services: | Forum | Review | PDF | Favorites | |
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