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Coupled order-parameter system on a scale-free network

Coupled order-parameter system on a scale-free network The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach, we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean-field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are nonzero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale-free network, there are notable differences for the amplitude ratios and the susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T < T c , when O ( n ) symmetry is present. This behavior is related to the appearance of Goldstone modes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review E American Physical Society (APS)

Coupled order-parameter system on a scale-free network

12 pages

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References (11)

Publisher
American Physical Society (APS)
Copyright
Copyright © 2009 The American Physical Society
ISSN
1550-2376
DOI
10.1103/PhysRevE.80.011108
pmid
19658654
Publisher site
See Article on Publisher Site

Abstract

The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach, we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean-field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are nonzero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale-free network, there are notable differences for the amplitude ratios and the susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T < T c , when O ( n ) symmetry is present. This behavior is related to the appearance of Goldstone modes.

Journal

Physical Review EAmerican Physical Society (APS)

Published: Jul 1, 2009

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