A note on the non-commutative laplace–varadhan integral lemma
This is the pre-published version harvested from ArXiv. The published version is located at http://www.worldscinet.com/rmp/22/2207/S0129055X10004089.html
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 , 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 , the result is a non-commutative extension of the Laplace–Varadhan asymptotic formula.
W De Roeck, C Maes, K Netocny, and L Rey-Bellet. "A note on the non-commutative laplace–varadhan integral lemma" Reviews in Mathematical Physics 22.7 (2010): 839-858.
Available at: http://works.bepress.com/luc_rey_bellet/5