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 ξ∝exp(A/T), where A asymptotically approaches 2π$S^2$ for large spin S, but $A_{S=1/2\mathrm{}}$≃1.16 and $A_{S=1\mathrm{}}$≃5.46. We mention the relevance of our results to recent experiments in ${\mathrm{La}}_2$${\mathrm{CuO}}_4$.