Low-dimensional Heisenberg magnets: Riemann zeta function regularization

2025/09/17 by Irkhin, V. Yu.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2509.13977

Abstract

The Riemann zeta function regularization is employed to extract finite temperature corrections to effective magnetic moment S^* 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^* 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.

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