Partition function zeros of the one-dimensional Blume-Capel model in transfer matrix formalism

Zeros of the partition function of the one-dimensional ferromagnetic and antiferromagnetic Blume-Capel models have been studied by using the transfer matrix method in the thermodynamic limit and for finite size chains. The equation for the distribution of zeros of the partition function in the thermodynamic limit is derived. The distribution of the Yang-Lee and Fisher zeros are studied for a variety of values of the parameters of the model. Densities of the Yang-Lee and Fisher zeros are investigated and a singular behavior of the corresponding densities of zeros at the edge points is shown. The edge singularity exponents are calculated analytically for the densities of the Yang-Lee and Fisher zeros. It is found that for both cases edge singularity exponents are universal and equal to sigma=-1/2.