Collège Doctoral - Doktorandenkollegien

Statistical Physics of Complex Systems

Coventry - Leipzig - Lviv - Nancy

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Title Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks
Authors M. Krasnytska, B. Berche, Holovatch Yu., R. Kenna
ArXivarxiv:1510.0053
Abstract We analyze the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P(k)∼k−λ. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee-Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ>5, reproduces the zeros for the Ising model on a complete graph. For 3<λ<5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee-Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3<λ<5. Whereas in the former case the zeros are purely imaginary, they have a non zero real part in latter case, so that the celebrated Lee-Yang circle theorem is violated.


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