A note on the non-commutative laplace–varadhan integral lemma

W De Roeck
C Maes
K Netocny
L Rey-Bellet, University of Massachusetts - Amherst

Article comments

This is the pre-published version harvested from ArXiv. The published version is located at http://www.worldscinet.com/rmp/22/2207/S0129055X10004089.html

Abstract

We continue the study of the free energy of quantum lattice spin systems where to the local Hamiltonian H an arbitrary mean field term is added, a polynomial function of the arithmetic mean of some local observables X and Y that do not necessarily commute. By slightly extending a recent paper by Hiai, Mosonyi, Ohno and Petz [10], we prove in general that the free energy is given by a variational principle over the range of the operators X and Y. As in [10], the result is a non-commutative extension of the Laplace–Varadhan asymptotic formula.