## Abstract

We study some properties of the Ising model in the plane of the complex (energy/temperature)-dependent variable u = e^{-4K}, where K = J/(k_{B}T), for nonzero external magnetic field, H. Exact results are given for the phase diagram in the u plane for the model in one dimension and on infinite-length quasi-one-dimensional strips. In the case of real h = H/(k_{B}T), these results provide new insights into features of our earlier study of this case. We also consider complex h = H/(k_{B}T) and μ = e^{-2h}. Calculations of complex-u zeros of the partition function on sections of the square lattice are presented. For the case of imaginary h, i.e., μ = e^{iθ}, we use exact results for the quasi-1D strips together with these partition function zeros for the model in 2D to infer some properties of the resultant phase diagram in the u plane. We find that in this case, the phase boundary contains a real line segment extending through part of the physical ferromagnetic interval 0 ≤ u ≤ 1, with a right-hand endpoint u_{rhe}at the temperature for which the Yang-Lee edge singularity occurs at μ = e^{±iθ}. Conformal field theory arguments are used to relate the singularities at u_{rhe}and the Yang-Lee edge.

Original language | English (US) |
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Article number | 135002 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 13 |

DOIs | |

State | Published - Apr 4 2008 |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- General Physics and Astronomy