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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Article number | 135001 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 49 |
Issue number | 13 |
Early online date | 17 Feb 2016 |
DOIs | |
Publication status | Published - 1 Apr 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/1510.00534Fingerprint
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Ralph Kenna
- Research Centre for Fluid and Complex Systems - Professor of Theoretical Physics
Person: Teaching and Research