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arXiv · 1012.4454

Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model

D. Dalmazi·F. L. Sa
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Abstract

We show here for the one-dimensional spin-1/2 ANNNI (axial-next-to-nearest-neighbor-Ising) model in an external magnetic field that the linear density of Yang-Lee zeros may diverge with critical exponent $\sigma = -2/3$ at the Yang-Lee edge singularity. The necessary condition for this unusual behavior is the triple degeneracy of the transfer matrix eigenvalues. If this condition is absent we have the usual value $\sigma = -1/2$. Analogous results have been found in the literature in the spin-1 Blume-Emery-Griffths model and in the three-state Potts model in a magnetic field with two complex components. Our results support the universality of $\sigma = -2/3$ which might be a one-dimensional footprint of a tricritical version of the Yang-Lee-Edge singularity possibly present also in higher-dimensional spin models.

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D. Dalmazi, F. L. Sa. 2010-12-20. Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model. https://doi.org/10.1103/physreve.82.051108

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