HALDANE-GAP IN THE QUASI-ONE-DIMENSIONAL NONLINEAR SIGMA-MODEL

This work studies the appearance of a Haldane gap in quasi-one-dimensi onal antiferromagnets in the long-wavelength limit, via the nonlinear sigma model. The mapping from the three-dimensional, integer-spin Heis enberg model to the nonlinear sigma model is explained, taking into ac count two antiferromagnetic couplings: one along the chain axis (J) an d one along the perpendicular planes (J(perpendicular-to)) of a cubic lattice. An implicit equation for the Haldane gap is derived, as a fun ction of temperature and coupling ratio J(perpendicular-to)/J. Solutio ns to these equations show the existence of a critical coupling ratio beyond which a gap exists only above a transition temperature TN. The cutoff dependence of these results is discussed.