Critical behavior at edge singularities in one-dimensional spin models

In ferromagnetic spin models above the critical temperature (T> Tcr) the partition function zeros accumulate at complex values of the magnetic field (HE) with a universal behavior for the density of zeros ρ (H) ∼ H- HE σ. The critical exponent σ is believed to be universal at each space dimension and it is related to the magnetic scaling exponent yh via σ= (d- yh) yh. In two dimensions we have yh =125 (σ=-16) while yh =2 (σ=-12) in d=1. For the one-dimensional Blume-Capel and Blume-Emery-Griffiths models we show here, for different temperatures, that a value yh =3 (σ=-23) can emerge if we have a triple degeneracy of the transfer matrix eigenvalues. © 2008 The American Physical Society.