Critical behavior at edge singularities in one-dimensional spin models.

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) approximately mid R:H-H_{E}mid R:;{sigma} . The critical exponent sigma is believed to be universal at each space dimension and it is related to the magnetic scaling exponent y_{h} via sigma=(d-y_{h})y_{h} . In two dimensions we have y_{h}=125(sigma=-16) while y_{h}=2(sigma=-12) in d=1 . For the one-dimensional Blume-Capel and Blume-Emery-Griffiths models we show here, for different temperatures, that a value y_{h}=3(sigma=-23) can emerge if we have a triple degeneracy of the transfer matrix eigenvalues.