A quasi-two-dimensional (2D) nonlinear sigma model (NLSM) is used to model the antiferromagnetism of the insulating layered undoped cuprate materials. As Chakravarty, Halperin, and Nelson (CHN) did for their 2D NLSM, we make a renormalization-group analysis of the quasi-2D NLSM. In contrast with CHN’s 2D model, the quasi-2D NLSM yields a nonzero Ne´el temperature so that our theoretical Ne´el temperatures can be fitted completely with the experimental ones. Our theoretical correlation lengths are fitted very well with the experimental ${\mathrm{La}}_2$${\mathrm{CuO}}_4$ data of the materials within 220 K above ${\mathit{T}}_{\mathit{N}}$.

• Received 13 January 1992

DOI:https://doi.org/10.1103/PhysRevB.45.10771