The behavior of ordered quantum Heisenberg antiferromagnets is analyzed from the nonlinear σ model in two and three dimensions. Many thermodynamic and dynamic properties are found to be universal at low temperatures and small magnetic fields. Finite-size effects are also investigated in detail; the results should be useful for analyzing numerical work on two-dimensional (2D) quantum antiferromagnets. The X-Y phase transition in 2D which is induced by a magnetic field is discussed. Applications to the ordered phase of solid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ are also given.

• Received 20 January 1989

DOI:https://doi.org/10.1103/PhysRevB.39.11783