The Yang-Lee edge singularity in spin models on connected and non-connected rings

Abstract

Renormalization group arguments based on a l phi(3) field theory lead us to expect a certain universal behavior for the density of partition function zeros in spin models with short-range interaction. Such universality has been tested analytically and numerically in different d = 1 and higher dimensional spin models. In d = 1, one finds usually the critical exponent sigma = -1/2. Recently, we have shown in the d = 1 Blume-Emery-Griffiths ( BEG) model on a periodic static lattice (one ring) that a new critical behavior with s = -2/3 can arise if we have a triple degeneracy of the transfer matrix eigenvalues. Here we define the d = 1 BEG model on a dynamic lattice consisting of connected and non-connected rings (non-periodic lattice) and check numerically that also in this case we have mostly sigma = -1/2 while the new value sigma = - 2/3 can arise under the same conditions of the static lattice (triple degeneracy) which is a strong check of universality of the new value of sigma. We also show that although such conditions are necessary, they are not sufficient to guarantee the new critical behavior.