Time Correlation Functions of Three Classical Heisenberg Spins on an Isosceles Triangle and on a Chain: Strong Effects of Broken Symmetry

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At 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 J₁, or on an isosceles triangle with a third, different exchange constant J₂. As T∞, 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 trinagle with J₁=J₂. At low T, the Fourier transforms of the two autocorrelation functions with J₁≠ J₂ show one and four modes, respectively. For a semi-infinite J₂/J₁ range, one mode is a central peak. At the origin of this range, this mode has a novel scaling form.