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

Abstract

Renormalization group arguments based on a ıφ3 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 σ = −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 σ = −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 σ = −1/2 while the new value σ = −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 σ. We also show that although such conditions are necessary, they are not sufficient to guarantee the new critical behavior.