Transition from quantum to classical Heisenberg trimers: Thermodynamics and time correlation functions

Details Transition from quantum to classical Heisenberg trimers: Thermodynamics and time correlation functions Transition from quantum to classical Heisenberg trimers: Thermodynamics and time correlation functions

1999-10-07

arxiv.org/abs/cond-mat/9910092v1

Physica A 278 (2000) 214

Physics

Condensed Matter

Statistical Mechanics

9 pages, 4 postscript figures, uses 'epsfig.sty'. Submitted to Physica A. More information available at http://www.physik.un

Scientific paper

10.1016/S0378-4371(99)00571-3

We focus on the transition from quantum to classical behavior in thermodynamic functions and time correlation functions of a system consisting of three identical quantum spins s that interact via isotropic Heisenberg exchange. The partition function and the zero-field magnetic susceptibility are readily shown to adopt their classical forms with increasing s. The behavior of the spin autocorrelation function (ACF) is more subtle. Unlike the classical Heisenberg trimer where the ACF approaches a unique non-zero limit for long times, for the quantum trimer the ACF is periodic in time. We present exact values of the time average over one period of the quantum trimer for s less or equal 7 and for infinite temperature. These averages differ from the long-time limit, (9/40)\ln3+(7/30), of the corresponding classical trimer by terms of order 1/(s*s). However, upon applying the Levin u-sequence acceleration method to our quantum results we can reproduce the classical value to six significant figures.

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