Density of Yang-Lee zeros for the Ising ferromagnet

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 ($L=3\sim 16$). 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.

arXiv commentto appear in Physical Review E

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• Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model
• Analyticity of the Ising susceptibility: An interpretation
• Condensation of Lee-Yang zeros in scalar field theory
• Yang-Lee Zeros of Certain Antiferromagnetic Models