Solutions for the T = 0 quantum spin glass transition in a metallic model with spin‐charge coupling

Abstract

AbstractWe solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – Jc (T = 0). The critical value Jc(T = 0) = 3/16pF−1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica‐overlap order parameter 〈Qab〉, a ≠ b, the diagonal 〈Qaa〉 is confirmed as order parameter by the result 〈Qaa〉 SP ∼ (δJ)β, β = 1, and its susceptibility χaaaa ∼(‐δJ)−γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Qaa〉, ∼ T is obtained exactly in the whole quantum disordered phase including the critical value.