## Abstract

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 X approximately 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}'= sigma _{s}=0 and beta _{s}= 1/4 , so that the scaling relation alpha _{s}'+2 beta _{s}+ gamma _{s}' 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.

Original language | English (US) |
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Article number | 012 |

Pages (from-to) | 1557-1583 |

Number of pages | 27 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 28 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 1995 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)