Rounding of first-order phase transitions and optimal cooperation in scale-free networks

M. Karsai, J. Ch Anglès D'Auriac, F. Iglói

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We consider the ferromagnetic large- q state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports of independent projects. The agents are found to be typically of two kinds: A fraction of m (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man's projects. It is shown rigorously that the homogeneous model has a strongly first-order phase transition, which turns to second-order for random interactions (benefits), the properties of which are studied numerically on the Barabási-Albert network. The distribution of finite-size transition points is characterized by a shift exponent, 1 ν ′ =0.26 (1), and by a different width exponent, 1 ν′ =0.18 (1), whereas the magnetization at the transition point scales with the size of the network, N, as m∼ N-x, with x=0.66 (1).

Original languageEnglish
Article number041107
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume76
Issue number4
DOIs
Publication statusPublished - Oct 3 2007

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First-order Phase Transition
Rounding
Scale-free Networks
Potts Model
Magnetization
Exponent
transition points
exponents
Complex Networks
magnetization
Optimise
Interaction
shift
interactions
Model

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Rounding of first-order phase transitions and optimal cooperation in scale-free networks. / Karsai, M.; D'Auriac, J. Ch Anglès; Iglói, F.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 76, No. 4, 041107, 03.10.2007.

Research output: Contribution to journalArticle

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