Nonlinear sigma model and quantum antiferromagnets

It is broadly viewed that the magnetism may play an important role in the high-Tc superconductivity in the lamellar CuO2 materials. In this paper, based on the one-loop analysis of the CP1 (or S2) nonlinear σ model as a low energy effective field theory of the Hubbard or the antiferromagnetic Heisenberg model, some magnetic properties of d-(space) dimensional quantum antiferromagnets are studied. For d≤1, or d≤2 at any nonzero temperature, long range Neel order (LRNO) disappears, in agreement with Mermin-Wagner-Coleman's theorem. For d = 3 in the weak coupling region, LRNO exists below the critical temperature TN(Neel temperature). TN decreases as the ratio (= α) of interlayer coupling over that within Cu - O layers becomes small. For the realistic case (α ≅ 10-5) the phase diagram and the behavior of magnetization and the spin correlation length as functions of temperature are investigated in detail. The results show that our anisotropic field theory model could give a reasonably well description of the magnetic properties indicated by some experiments on La2CuO4. (author)