  Let H be a self-adjoint operator such that exp(-aH) is of trace class for
some a<1. Let V be a symmetric operator, Kato bounded relative to H. We show
that log Tr[exp(-H+xV)] is a real analytic function of x in a hood of x=0. We
show that the Gibbs states of H+xV form a real analytic Banach manifold. This
work has been extended in math-ph/9910031.
