Dynamical Properties of the Spherical Model in the Low-Temperature and Critical Regions

Abstract

The properties of the time-dependent spin correlation functions are investigated for the spherical model of the classical magnetic system. Equations for the correlation functions are derived by a diagrammatic analysis. The lowest-order approximation is for $T>\mathrm{}{T}_c$ identical to the equation derived by Resibois and De Leener for the Weiss limit of the Heisenberg model. Attention has been given to the hydrodynamic regime along the line of spontaneous magnetization from $T=0\mathrm{}$ up to $T=T_c$, where spin-wave frequencies and damping rates as well as the "diffusive" behavior have been calculated to lowest order in the wave number. The dynamical scaling problem is examined within this diagrammatic analysis. The scaling properties and the equations determining the homogeneous correlation function are established explicitly.