Dynamics of Vector Spin-Glasses

A description of spin-glass dynamics at low temperatures, based on a "harmonic" theory, is presented. The Hamiltonian is approximated by a quadratic form in the spin deviations from a particular local minimum, and diagonalized. The dynamics is governed by the eigenvalue distribution $\rho \left(\lambda \right)$. The validity of this description is supported by computer simulations. These suggest that $\rho \mathrm{}\left(0\right)\mathrm{}\ne 0$ in two and three dimensions, implying a logarithmic decay in time of the spin autocorrelation function at low temperatures.