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

Abstract

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 $J_1$, or on an isosceles triangle with a third, different exchange constant $J_2$. As $T\rightrarrow\infty$, 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 $J_1=J_2$. At low $T$, the Fourier transforms of the two autocorrelation functions with $J_1\ne J_2$ 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 a novel scaling form.

9 pages, 14 figures, accepted for publication in Phys. Rev. B

References in corpus (3)

• Heisenberg Dimer Single Molecule Magnets in a Strong Magnetic Field
• Zero-field Time Correlation Functions of Four Classical Heisenberg Spins on a Ring
• Exact Time Autocorrelation Function of the N-Spin Classical Heisenberg Equivalent Neighbor Model

Cited by in corpus (7)

• Neutron Scattering and Magnetic Observables for S = 1/2 Molecular Magnets
• Generalization of polarized spin excitations for asymmetric dimeric systems
• Thermodynamics and spin mapping of quantum excitations in a Heisenberg spin heptamer
• The general spin triangle
• Thermodynamics of the spin square
• Thermodynamics of the classical spin triangle
• Exact time correlation functions for N classical Heisenberg spins in the `squashed' equivalent neighbor model