Density of Yang-Lee zeros for the Ising ferromagnet

Details Density of Yang-Lee zeros for the Ising ferromagnet Density of Yang-Lee zeros for the Ising ferromagnet

2006-07-11

arxiv.org/abs/cond-mat/0607257v1

Physical Review E 74 (2006) 011119

Physics

Condensed Matter

Statistical Mechanics

to appear in Physical Review E

Scientific paper

10.1103/PhysRevE.74.011119

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.

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