Quantum Heisenberg Ferromagnets in One and Two Dimensions at Low Temperature

Abstract

Modifying the spin-wave theory in the three-dimensional Heisenberg ferromagnet, we propose a simple approximation to investigate the low-temperature thermodynamics of one- and two-dimensional Heisenberg ferromagnets H = -J Σ≪ij> (SiSj - S2), where S is the spin quantum number. We regard that the system is an ideal Bose gas with density S. For one-dimensional chain we get the free energy and the susceptibility per site: Formula At S = 1/2 these coincide with the numerical results of the Bethe-ansatz integral equation. The susceptibility has not logarithmic correction contrary to a recent proposal by Schlottmann. For two-dimensional square lattice we get: Formula