Functional integral theories of low-dimensional quantum Heisenberg models

We investigate the low-temperature properties of the quantum Heisenberg models, both ferromagnetic and antiferromagnetic, in one and two dimensions. We study two different large-N formulations, using Schwinger bosons and S= (1/2 fermions, and solve for their low-order thermodynamic properties. Comparison with exact solutions in one dimension demonstrates the applicability of this expansion to the physical models at N=2. For the square lattice, we find at the mean-field level a low-temperature correlation length which behaves as (A/T), where A asymptotically approaches 2S^2 for large spin S, but Aₒ=₁/₂1. 16 and Aₒ=₁5. 46. We mention the relevance of our results to recent experiments in La₂CuO₄.