Abstract
We analyze the partition function of the Ising model on graphs of twodifferent types: complete graphs, wherein all nodes are mutually linked and annealedscalefree 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 LeeYang zeros respectively). For the model on anannealed scalefree 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 λdependent angle at which the Fisher zerosimpact onto the real temperature axis. This, in turn, gives access to the λdependentuniversal values of the critical exponents and critical amplitudes ratios. Our analysisof the LeeYang zeros reveals a difference in their behaviour for the Ising model on acomplete graph and on an annealed scalefree 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 LeeYang circle theorem is violated.
Original language  English 

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