Phase transitions on complex networks

Abstract : The thesis is devoted to the investigation of the critical behavior of spin models on a scale-free network with a power-law node-degree probability distribution P(k) ∼ k^(-λ),, in presence of quenched or annealed disorder, and on a complete graph. For the Potts model on a scale-free network in terms of inhomogeneous mean-field approach we found the set of critical exponents, critical amplitude ratios and scaling functions, which appear to be dependent on the probability distribution decay exponent λ. In that sense λ is manifested to be one of the global parameters which define the universality class. Along with the traditional theory of complex networks by inhomogeneous mean-field method, we use for the first time the method of partition function zeros analysis in the complex plane. Unusual behavior was observed for a number of universal features, such as the angle of Fisher zeros condensation φ and the exponent σ which appear to be λ -dependent. We also observe that the Lee-Yang circle theorem is violated in the region 3 < λ < 5 for the Ising model on an annealed scale-free network.
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Submitted on : Tuesday, October 18, 2016 - 9:30:11 AM
Last modification on : Wednesday, September 4, 2019 - 2:06:03 PM

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  • HAL Id : tel-01383083, version 1

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Mariana Krasnytska. Phase transitions on complex networks. Physics [physics]. Université de Lorraine; Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 2016. English. ⟨tel-01383083⟩

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