## Abstract

We study complex-temperature singularities of the Ising model on the triangular and honeycomb lattices. We first discuss the complex-T phases and their boundaries. From exact results, we determine the complex-T singularities in the specific heat and magnetization. For the triangular lattice we discuss the implications of the divergence of the magnetization at the point u = -1/3 (where u = z^{2} = e^{-4K}) and extend a previous study by Guttmann of the susceptibility at this point with the use of differential approximants. For the honeycomb lattice, from an analysis of low-temperature series expansions, we have found evidence that the uniform and staggered susceptibilities χ̄ and χ̄^{(a)} both have divergent singularities at z = -1 ≡ z_{ℓ}, and our numerical values for the exponents are consistent with the hypothesis that the exact values are γ′_{ℓ} = γ′_{ℓ,a} = 5/2. The critical amplitudes at this singularity were calculated. Using our exact results for α′ and β together with numerical values for γ′ from series analyses, we find that the exponent relation α′ + 2β + γ′ = 2 is violated at z = -1 on the honeycomb lattice; the right-hand side is consistent with being equal to 4 rather than 2. The connections of the critical exponents at these two singularities on the triangular and honeycomb lattice are discussed.

Original language | English (US) |
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Pages (from-to) | 803-823 |

Number of pages | 21 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 29 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1996 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

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