Complex-Temperature Singularities of the Susceptibility in the $d=2$ Ising Model. I. Square Lattice

Details Complex-Temperature Singularities of the Susceptibility in the $d=2$ Ising Model. I. Square Lattice Complex-Temperature Singularities of the Susceptibility in the $d=2$ Ising Model. I. Square Lattice

1994-08-29

arxiv.org/abs/hep-lat/9408020v4

J.Phys. A28 (1995) 1557-1584

Physics

High Energy Physics

High Energy Physics - Lattice

Latex file, 27 pages of text plus figures appended to file. ITP-SB-94-37. (further results added to sections 4, 7)

Scientific paper

10.1088/0305-4470/28/6/012

We investigate the complex-temperature singularities of the susceptibility of the 2D Ising model on a square lattice. From an analysis of low-temperature series expansions, we find evidence that as one approaches the point $u=u_s=-1$ (where $u=e^{-4K}$) from within the complex extensions of the FM or AFM phases, the susceptibility has a divergent singularity of the form $\chi \sim A_s'(1+u)^{-\gamma_s'}$ with exponent $\gamma_s'=3/2$. The critical amplitude $A_s'$ is calculated. Other critical exponents are found to be $\alpha_s'=\alpha_s=0$ and $\beta_s=1/4$, so that the scaling relation $\alpha_s'+2\beta_s+\gamma_s'=2$ is satisfied. However, using exact results for $\beta_s$ on the square, triangular, and honeycomb lattices, we show that universality is violated at this singularity: $\beta_s$ is lattice-dependent. Finally, from an analysis of spin-spin correlation functions, we demonstrate that the correlation length and hence susceptibility are finite as one approaches the point $u=-1$ from within the symmetric phase. This is confirmed by an explicit study of high-temperature series expansions.

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