Showing papers by "Herbert B. Callen published in 1972"

Point-Group Symmetry and the Impurity Problem

Abstract: It is shown that in a pure crystal the density of states of a given point-group symmetry (that is, belonging to a given row of a given irreducible representation of the point group) is simply $(\frac{{d}_{\ensuremath{\Gamma}}}{p}){g}^{0}(E)$, where ${g}^{0}(E)$ is the familiar over-all density of states, ${d}_{\ensuremath{\Gamma}}$ is the dimensionality of the representation, and $p$ is the order of the group. Point-group symmetry is incorporated into Green's-function theory to define Green's functions which propagate excitations of particular symmetries from shell to shell (rather than from site to site). Both simple crystal Green's functions and two-time thermodynamic Green's functions are considered, and the ferromagnetic-impurity problem is formulated in terms of such Green's functions (at $T=0$ and at arbitrary temperatures, respectively). The analysis is illustrated explicitly for a fcc ferromagnet with first- and second-nearest-neighbor exchange.