R. F. Streater
Published 1999-10-22, updated 1999-10-27Version 2
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.
Comments: 12 pages LATEX; to appear in "Stochastic processes, physics and geometry: new interplays"; eds. F. Gesztesy, S. Paycha and H. Holden. Canad. Math. Soc. In this replacement, I have made clear that it is the partition function that possesses a convergent power series with the given radius of convergence. The free-energy is real analytic only in an unspecified hood of the real axis
The information manifold for relatively bounded forms
Uniqueness of Gibbs states of a quantum system on graphs
A Mermin--Wagner theorem for Gibbs states on Lorentzian triangulations
