The partition function zeros of the anisotropic Ising model with multisite interactions on a zigzag ladder

It is shown that the spin-12 anisotropic Ising model with multisite interactions on a zigzag ladder may be mapped into the one dimensional spin-12 Axial-Next-Nearest-Neighbor Ising (ANNNI) model with multisite interactions. The partition function zeros of the ANNNI model with multisite interactions are investigated. A comprehensive analysis of the partition function zeros of the ANNNI model with and without three-site interactions on a zigzag ladder is done using the transfer matrix method. Analytical equations for the distribution of the partition function zeros in the complex magnetic field (Yang–Lee zeros) and temperature (Fisher zeros) planes are derived. The Yang–Lee and Fisher zeros distributions are studied numerically for a variety of values of the model parameters. The densities of the Yang–Lee and Fisher zeros are studied and the corresponding edge singularity exponents are calculated. It is shown that the introduction of three-site interaction terms in the ANNNI model leads to a simpler distribution of the partition function zeros. For example, the Yang–Lee zeros tend to a circular distribution when increasing by modulus the three-site interactions term coefficient. It is found that the Yang–Lee and Fisher edge singularity exponents are universal and equal to each other, σ=−12.