Long-wavelength Structure Research Articles

Long-wavelength dynamic response of the Heisenberg-Mattis model

The Heisenberg-Mattis model is the simplest prototype of a concentrated ferromagnetic-antiferromagnetic alloy having a low-temperature cooperative magnetic structure without average periodic order of the physical spins yet with strong non-trivial disorder in its linearised classical equations of motion. Within this classical approximation the dominant long-wavelength structure of the dynamic transverse spin response function is calculated exactly and found to have significant dimension dependence. In three dimensions quasi-propagation is found with linear dispersion and quadratic disorder damping. In one dimension it has strongly damped character with q4/3 scaling.

Comments on Long-Wavelength Excitations and Structure Functions in the Theory of LiquidHe4atT=0

Polynomial approximations for the liquid structure function $S(k)$ and the energy of an elementary excitation $\ensuremath{\epsilon}(k)$ are found to contain both odd and even powers of $k$ if the interatomic potential falls off asymptotically as ${r}^{\ensuremath{-}6}$. The proof is given under conditions of low density and weak interaction and hence has only suggestive force in applications to the real superfluid.