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∣\sg. The critical exponent \sg is believed to be universal at each space dimension and it is related to the magnetic scaling exponent yh via \sg=(d−yh)/yh. In two dimensions we have yh=12/5(\sg=−1/6) while yh=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 yh=3(\sg=−2/3) can emerge if we have a triple degeneracy of the transfer matrix eigenvalues.
@article{arxiv.0809.4510,
title = {Critical behavior at edge singularities in one dimensional spin models},
author = {D. Dalmazi and F. L. Sá},
journal= {arXiv preprint arXiv:0809.4510},
year = {2009}
}