Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice

Details Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice Distribution of partition function zeros of the $\pm J$ model on the Bethe lattice

2010-01-27

arxiv.org/abs/1001.4873v2

J. Phys. A: Math. Theor. 43 (2010) 285002

Physics

Condensed Matter

Disordered Systems and Neural Networks

23 pages, 12 figures

Scientific paper

10.1088/1751-8113/43/28/285002

The distribution of partition function zeros is studied for the $\pm J$ model of spin glasses on the Bethe lattice. We find a relation between the distribution of complex cavity fields and the density of zeros, which enables us to obtain the density of zeros for the infinite system size by using the cavity method. The phase boundaries thus derived from the location of the zeros are consistent with the results of direct analytical calculations. This is the first example in which the spin glass transition is related to the distribution of zeros directly in the thermodynamical limit. We clarify how the spin glass transition is characterized by the zeros of the partition function. It is also shown that in the spin glass phase a continuous distribution of singularities touches the axes of real field and temperature.

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