CPA approach to the random Ising model in a transverse field

Abstract

The dynamics of a two-component Ising model in a transverse field (IMTF) with randomness during both in the transverse field and the Ising coupling is treated within the single-site coherent potential approximation (CPA). The authors deal primarily with the polarized phase; they replace the fluctuating longitudinal component of the molecular field by two effective parameters, one for each species, which are determined self-consistently. The CPA spectra of the collective spin excitations are found analytically in the dilute case using a Hubbard model density for the Ising interaction, and are also calculated numerically for the general two-component IMTF. It is shown that the static susceptibility cannot diverge within the single site CPA. Characterizing the phase transition by the softening of the lowest mode in the spectrum. The stability conditions for the polarized phase at T=O are then determined.