Articles dans des revues à comité de lecture
|Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks|
|M. Krasnytska, B. Berche, Holovatch Yu., R. Kenna|
|J. Phys. A: Math. Theor. 49 (2016) 135001|
|DOI : 10.1088/1751-8113/49/13/135001|
|ArXiv : arxiv:1510.00534 [PDF]|
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)âˆ¼kâˆ’Î». 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 Î»>5, reproduces the zeros for the Ising model on a complete graph. For 3<Î»<5 we derive the Î»-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the Î»-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<Î»<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.