A Feynman-Kac formula for the quantum Heisenberg ferromagnet. II (Q2276817)

In part I of this work [the authors, ibid. 131, No.3, 465-494 (1990; Zbl 0715.58005)] heat kernel representations for the partition function of the Euclidean lattice field theory based on the Heisenberg ferromagnet were given. In the present article the authors derive Feynman-Kac representations for the heat kernels, first for the one-lattice point theory and then for the full interacting theory on an arbitrary finite lattice. Methods of stochastic analysis due to \textit{J.-M. Bismut} [J. Funct. Anal. 57, 56-99 (1984; Zbl 0538.58033)] are employed. Finally classical limit theorems for the purely bosonic sector of the theory are presented.