Correlation functionals of infinite volume quantum spin systems

The existence and analyticity of the correlation functionals of a quantum lattice in the infinite volume limit is proved. The result is valid at sufficiently high temperatures and for a large class of interactions. Our method estimates the kernelK for a set of Kirkwood-Salzburg equations. While a naive estimate would indicate that K=, we take into account cancellations between different contributions toK in order to show that for sufficiently high temperatures K <1, and this estimate is independent of the volume of the system.Supported in part by the Air Force Office of Scientific Research.