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Solutions for the T = 0 quantum spin glass transition in a metallic model with spin‐charge coupling
Author(s) -
Oppermann R.,
Binderberger M.
Publication year - 1994
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19945060607
Subject(s) - condensed matter physics , spin glass , physics , spin (aerodynamics) , charge (physics) , saddle point , quantum critical point , coupling (piping) , quantum phase transition , quantum spin liquid , quantum mechanics , phase transition , thermodynamics , materials science , spin polarization , electron , geometry , mathematics , metallurgy
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.