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

We study the momentum dependence of static magnetic susceptibility chi (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 chi(q) proportional to {q(2) + xi(-2) [1 + f (q xi)]}(-1+eta/2), where xi 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) similar or equal to (2B(4)/N)(x)(4-d); the absolute value of the coefficient B-4 increases with d at d > 5/2. Using NLSM, we obtain the contribution of the anomalous term xi(-2) f (q xi) to the critical exponent nu, comparing it to the contribution of the nonanalytical dependence, originating from the critical exponent eta (the obtained critical exponents nu and eta 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 v in the limit d -> 4.

Automated summary

This study investigates the momentum dependence of static magnetic susceptibility in the paramagnetic phase of Heisenberg magnets and its relation to critical behavior within the nonlinear sigma model at finite dimension. The research reveals the contribution of anomalous terms to critical exponent nu and the dominance of such terms in determining the 1/N correction to the critical exponent v in certain dimension ranges.