Low-dimensional Heisenberg magnets: Riemann zeta function regularization

Abstract

The Riemann zeta function regularization is employed to extract finite temperature corrections to effective magnetic moment $S^{\ast }$ of one- and two-dimensional Heisenberg ferro- and antiferromagnets. Whereas for the one-dimensional ferromagnet we obtain the usual $T^{1/2}$ spin-wave dependence, for the antiferromagnetic chain the dependence is described by a generalized incomplete Riemann function. The quantity $S^{\ast }$ determines strong short-range magnetic order in the absence of long-range order, in particular the correlation length. For the one-dimensional ferromagnet, the results are confirmed by the self-consistent spin-wave theory and Monte Carlo simulations by Takahashi et al.

4 pages

References in corpus (6)

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• Physics of the Riemann Hypothesis
• Euler - Heisenberg effective action and magnetoelectric effect in multilayer graphene
• Strong short-range magnetic order in a frustrated FCC lattice and its possible role in the iron structural transformation
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