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

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

2010-12-20

arxiv.org/abs/1012.4454v1

Phys. Rev. E 82 (2010)051108

Physics

Condensed Matter

Statistical Mechanics

19 pages, 6 figures, 1 table

Scientific paper

10.1103/PhysRevE.82.051108

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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