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Abstract

At an arbitrary temperature T, we solve for the dynamics of single molecule magnets composed of three classical Heisenberg spins either on a chain with two equal exchange constants J(1), or on an isosceles triangle with a third, different exchange constant J(2). As T-->infinity, the Fourier transforms and long-time asymptotic behaviors of the two-spin time correlation functions are evaluated exactly. The lack of translational symmetry on a chain or an isosceles triangle yields time correlation functions that differ strikingly from those on an equilateral triangle with J(1)=J(2). At low T, the Fourier transforms of the two autocorrelation functions with J(1)not equalJ(2) show one and four modes, respectively. For a semi- infinite J(2)/J(1) range, one mode is a central peak. At the origin of this range, this mode has an interesting scaling form.