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 xiproportionalexp(A/T), where A asymptotically approaches 2..pi..S/sup 2/ for large spin S, but A/sub S//sub //sub = //sub 1/2/approx. =1.16 and A/sub S//sub //sub = //sub 1/approx. =5.46. We mention the relevance of our results to recent experiments in La/sub 2/CuO/sub 4/.