Few-dimensional Heisenberg ferromagnets at low temperature

A simple approximation for one- and two-dimensional Heisenberg ferromagnets is proposed. This is a modification of the spin-wave theory for a three-dimensional ferromagnet and is expected to give correct low-temperature properties. The free energy and susceptibility of the linear chain are expanded in powers of square root of temperature. At S=(1/2) the results agree excellently with those of Bethe-Ansatz integral equations. The susceptibility of the two-dimensional square lattice diverges as exp(4\ensuremath{\pi}${\mathrm{JS}}^{2}$/T).

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