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

We 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 – J c ( T = 0). The critical value J c ( T = 0) = 3/16 p F −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 〈 Q ab 〉, a ≠ b , the diagonal 〈 Q aa 〉 is confirmed as order parameter by the result 〈 Q aa 〉 SP ∼ (δJ) β , β = 1, and its susceptibility χ aaaa ∼(‐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 〈 Q aa 〉, ∼ T is obtained exactly in the whole quantum disordered phase including the critical value.