## Abstract

We computed the variance 〈x^{2}〉- 〈x〉^{2} of the operator x=E_{q}E_{-q} in which E_{q}=ΣS_{r}·S_{r+1}e^{iqr} for a one dimensional classical Heisenberg chain. We show that (〈x ^{2}〉-〈x〉^{2})/〈x〉^{2} is of order 1, not of order 1/N as expected for a thermodynamic variable. This differs from earlier reported results for this variance. We find a similar result for the one-dimensional Ising and x-y models and establish a general condition for the correlation functions which causes such a result to oaccur. The large variance means that numerical calculations of 〈E_{q}E _{-q}(t) 〉 must be done carefully to produce reliable results. We introduce a new method to calculate 〈E_{q}E_{-q}(t) 〉 which avoids this problem. The method gives excellent results for the known values at t=0. We present results for 〈E_{q}E_{-q}(t) 〉 using this new method. They contain some features which are not yet fully understood.

Original language | English (US) |
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Pages (from-to) | 1768-1770 |

Number of pages | 3 |

Journal | Journal of Applied Physics |

Volume | 50 |

Issue number | B3 |

DOIs | |

State | Published - Dec 1 1979 |