## Abstract

Although the physical properties of the 2D and 1D Ising models are quite different, we point out an interesting connection between their complex-temperature phase diagrams. We carry out an exact determination of the complex-temperature phase diagram for the 1D Ising model for arbitrary spin s and show that in the u_{s} = e^{ -K s2} plane (i) it consists of N_{c,1D} = 4s^{2} infinite regions separated by an equal number of boundary curves where the free energy is nonanalytic; (ii) these curves extend from the origin to complex infinity, and in both limits are oriented along the angles θ_{n} = (1 + 2n)π 4s^{2}, for n = 0,...,4s^{2} - 1; (iii) of these curves, there are N_{c,NE,1D} = N_{c,NW,1D} = [s^{2}] in the first and second (NE and NW) quadrants; and (iv) there is a boundary curve (line) along the negative real u_{s} axis if and only if s is half-integral. We note a close relation between these results and the number of arcs of zeros protruding into the FM phase in our recent calculation of partition function zeros for the 2D spin s Ising model.

Original language | English (US) |
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Pages (from-to) | 353-358 |

Number of pages | 6 |

Journal | Physics Letters A |

Volume | 204 |

Issue number | 5-6 |

DOIs | |

State | Published - Aug 28 1995 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- General Physics and Astronomy