  In ferromagnetic spin models above the critical temperature ($T > T_{cr}$)
the partition function zeros accumulate at complex values of the magnetic field
($H_E$) with a universal behavior for the density of zeros $\rho (H) \sim | H -
H_E |^{\sg}$. The critical exponent $\sg$ is believed to be universal at each
space dimension and it is related to the magnetic scaling exponent $y_h$ via
$\sg = (d-y_h)/y_h$. In two dimensions we have $y_h=12/5 (\sg = -1/6)$ while
$y_h=2 (\sg=-1/2)$ in $d=1$. For the one dimensional Blume-Capel and
Blume-Emery-Griffiths models we show here, for different temperatures, that a
new value $y_h=3 (\sg =-2/3)$ can emerge if we have a triple degeneracy of the
transfer matrix eigenvalues.
