Critical behavior at edge singularities in one-dimensional spin models

Abstract

In ferromagnetic spin models above the critical temperature (T>Tcr) 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) similar to vertical bar H-HE vertical bar(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) = 12/5 (sigma = -1/6) while y(h) = 2 (sigma = -1/2) 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 = -2/3) can emerge if we have a triple degeneracy of the transfer matrix eigenvalues.