Based on the equivalence between the spin-(1/2 Heisenberg antiferromagnet and the hard-core Bose gas we investigate a Jastrow trial wave function, which has proven to give an excellent ground-state energy. In this paper the energy and the spin-spin correlation functions are evaluated analytically by representing them in terms of partition sums of two-dimensional Ising-like models expressed as integrals over Grassmann variables.
von der Linden, W., Ziegler, M., & Horsch, P. (1989). Exact evaluation of the nearest-neighbor Jastrow wave function for the two-dimensional spin-(1/2 Heisenberg antiferromagnet. Physical review / E, 40(10), 7435. https://doi.org/10.1103/PhysRevB.40.7435