Dynamics of the Iongitudinal spin for the three-dimensional, spin-½ Ising model in a transverse field

Abstract

The dynamics of the Iongitudinal (i.e., parrallel to the $z$ axis) spin fluctuations of the three-dimensional Ising model in a transverse field, $H=-\Gamma \Sigma i^{}{S}_i^x-\left(\frac{1}{2}\right)\Sigma {\mathrm{ij}}^{}{J}_{\mathrm{ij}}{S}_i^z{S}_j^z$, is studied. An approximate expression for the relaxation shape function is given which gives a simple but realistic view of the dynamics for the entire temperature range $T_c<T<\mathrm{}\infty$. Plots of the shape function are obtained and analyzed.