Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks

M. Krasnytska, B. Berche, Y. Holovatch, Ralph Kenna

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Abstract

We analyze the partition function of the Ising model on graphs of twodifferent types: complete graphs, wherein all nodes are mutually linked and annealedscale-free networks for which the degree distribution decays as P(k) ∼ k−λ. We areinterested in zeros of the partition function in the cases of complex temperature orcomplex external field (Fisher and Lee-Yang zeros respectively). For the model on anannealed scale-free network, we find an integral representation for the partition functionwhich, in the case λ > 5, reproduces the zeros for the Ising model on a completegraph. For 3 <λ <5 we derive the λ-dependent angle at which the Fisher zerosimpact onto the real temperature axis. This, in turn, gives access to the λ-dependentuniversal values of the critical exponents and critical amplitudes ratios. Our analysisof the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on acomplete graph and on an annealed scale-free network when 3 <λ <5. Whereas inthe former case the zeros are purely imaginary, they have a non zero real part in lattercase, so that the celebrated Lee-Yang circle theorem is violated.
Original languageEnglish
Pages (from-to)135001
JournalJournal of Physics A: Mathematical and Theoretical
Volume49
Issue number13
DOIs
Publication statusPublished - 17 Feb 2016

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Ising model
Scale-free Networks
Complex networks
Partition Function
Complete Graph
Ising Model
partitions
Zero
theorems
Circle theorem
exponents
Temperature
temperature
Degree Distribution
decay
Graph in graph theory
Temperature Field
Integral Representation
Critical Exponents
External Field

Bibliographical note

Due to publisher policy, the full text will not be available on the repository until 17th February 2017. The full text can, however, be found online here :http://arxiv.org/abs/1510.00534

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Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks. / Krasnytska, M.; Berche, B.; Holovatch, Y.; Kenna, Ralph.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 49, No. 13, 17.02.2016, p. 135001.

Research output: Contribution to journalArticle

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