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

We focus on the transition from quantum to classical behavior in thermodyna mic functions and time correlation functions of a system consisting of thre e identical quantum spins s that interact via isotropic Heisenberg exchange . The partition function and the zero-field magnetic susceptibility are rea dily shown to adopt their classical forms with increasing s. The behavior o f the spin autocorrelation function (ACF) is more subtle. Unlike the classi cal 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 than or equal to 7 and for infinite temperature. These averages diff er from the long-time limit, (9/40)ln 3 (7/30), of the corresponding classi cal trimer by terms of order 1/s(2). However, upon applying the Levin u-seq uence acceleration method to our quantum results we can reproduce the class ical value to six significant figures. (C) 2000 Elsevier Science B.V. All r ights reserved.