Fluctuations in the energy-energy correlation function of one-dimensional magnetic models

D. Bowman, J. W. Halley

Research output: Contribution to journalArticlepeer-review


We computed the variance 〈x2〉- 〈x〉2 of the operator x=EqE-q in which Eq=ΣSr·Sr+1eiqr 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 〈EqE -q(t) 〉 must be done carefully to produce reliable results. We introduce a new method to calculate 〈EqE-q(t) 〉 which avoids this problem. The method gives excellent results for the known values at t=0. We present results for 〈EqE-q(t) 〉 using this new method. They contain some features which are not yet fully understood.

Original languageEnglish (US)
Pages (from-to)1768-1770
Number of pages3
JournalJournal of Applied Physics
Issue numberB3
StatePublished - Dec 1 1979


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