Nonanalytic momentum dependence of spin susceptibility for Heisenberg magnets in the paramagnetic phase and its effect on critical exponents

• Published in: Physical review. B 2021-02, Vol.103 (5), p.1, Article 054415
• Main Author: Katanin, A. A.
• Format: Article
• Language: English
• Subjects: Dependence; Exponents; Field theory; Magnetic permeability; Magnets; Momentum; Quantum theory
• ISSN: 2469-9950; 2469-9969
• DOI: 10.1103/PhysRevB.103.054415

We study the momentum dependence of static magnetic susceptibility χ(q) in the paramagnetic phase of Heisenberg magnets and its relation to critical behavior within the nonlinear sigma model (NLSM) at arbitrary dimension 2 < d < 4. In the first order of 1/N expansion, where N is the number of spin components, we find χ(q) ∝ {q2+ξ−2[1 + f(qξ)]}−1+η/2, where ξ is the correlation length, q is the momentum, measured from the magnetic wave vector, and the universal scaling function f (x) describes the deviation from the standard Landau-Ginzburg momentum dependence. In agreement with previous studies at large x we find f(x≫ 1) ≃ (2B4/N)x4−d; the absolute value of the coefficient B4 increases with d at d > 5/2. Using NLSM, we obtain the contribution of the "anomalous" term ξ−2f (qξ) to the critical exponent ν, comparing it to the contribution of the nonanalytical dependence, originating from the critical exponent η (the obtained critical exponents ν and η agree with previous studies). In the range 3 ≤ d < 4 we find that the former contribution dominates and fully determines the 1/N correction to the critical exponent ν in the limit d → 4.