Density of Yang-Lee zeros for the Ising ferromagnet

TL;DR

This paper analyzes the distribution of Yang-Lee zeros in the Ising ferromagnet on finite square lattices, distinguishing phase transition types and detecting edge singularities through exact calculations.

Contribution

It provides exact finite-size calculations of Yang-Lee zero densities for the square-lattice Ising model, identifying different phase transition classes and the Yang-Lee edge singularity.

Findings

Distinguished phase transition types via zero density analysis.

Detected Yang-Lee edge singularity at high temperatures.

Discussed phase transition identification in small systems.

Abstract

The densities of Yang-Lee zeros for the Ising ferromagnet on the $L\times L$ square lattice are evaluated from the exact grand partition functions ($L=3\sim16$). The properties of the density of Yang-Lee zeros are discussed as a function of temperature $T$ and system size $L$. The three different classes of phase transitions for the Ising ferromagnet, first-order phase transition, second-order phase transition, and Yang-Lee edge singularity, are clearly distinguished by estimating the magnetic scaling exponent $y_h$ from the densities of zeros for finite-size systems. The divergence of the density of zeros at Yang-Lee edge in high temperatures (Yang-Lee edge singularity), which has been detected only by the series expansion until now for the square-lattice Ising ferromagnet, is obtained from the finite-size data. The identification of the orders of phase transitions in small systems is also discussed using the density of Yang-Lee zeros.