## Abstract

We study the truncation of the Mori continued fraction for the two-spin spectral function of the XY model in various schemes suggested by the 3-pole approximation. These schemes are (i) a fully consistent version of the 3-pole approximation; (ii) 5-pole approximation (not fully consistent); and (iii) 5-pole approximate (fully consistent). We establish the equilivalence between the fully consistent 3-pole approximation and the Bennett-Martin approximation. Finally, we calculate the time-dependent spin-spin correlation function for the classical Heisenberg model in both versions of the 3-pole approximation and compare it with the exact spin-spin correlation function obtained by direct numerical calculation in one dimension.

Original language | English (US) |
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Pages (from-to) | 1269-1274 |

Number of pages | 6 |

Journal | Journal of Physics and Chemistry of Solids |

Volume | 38 |

Issue number | 11 |

DOIs | |

State | Published - 1977 |

Externally published | Yes |

### Bibliographical note

Funding Information:tResearch supportedi n part by NSF Grant 34890 and by the Bush Foundation. $We have taken F(k,t) and consequently K,(t) to be even functions of f as in Refs. [5,6].