### 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 language | English |
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Pages (from-to) | 135001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 13 |

DOIs | |

Publication status | Published - 17 Feb 2016 |

### 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## Fingerprint Dive into the research topics of 'Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks'. Together they form a unique fingerprint.

## Cite this

Krasnytska, M., Berche, B., Holovatch, Y., & Kenna, R. (2016). Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks.

*Journal of Physics A: Mathematical and Theoretical*,*49*(13), 135001. https://doi.org/10.1088/1751-8113/49/13/135001