  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.
