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

TL;DR

This paper investigates the Yang-Lee edge singularity in the one-dimensional ANNNI model, revealing an unusual divergence with a critical exponent of -2/3 under specific eigenvalue degeneracy conditions, suggesting universality and potential links to higher-dimensional models.

Contribution

It demonstrates the occurrence of an unusual Yang-Lee edge singularity with exponent -2/3 in the 1D ANNNI model, extending the understanding of universality in spin models.

Findings

Critical exponent $\sigma = -2/3$ at the Yang-Lee edge for specific conditions.

Normal critical exponent $\sigma = -1/2$ when conditions are not met.

Supports universality of the $\sigma = -2/3$ exponent across models.

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.