A note on the non-commutative Laplace-Varadhan integral lemma
Mathematical Physics
2009-08-29 v2 math.MP
Abstract
We continue the study of the free energy of quantum lattice spin systems where to the local Hamiltonian an arbitrary mean field term is added, a polynomial function of the arithmetic mean of some local observables and that do not necessarily commute. By slightly extending a recent paper by Hiai, Mosonyi, Ohno and Petz [9], we prove in general that the free energy is given by a variational principle over the range of the operators and . As in [9], the result is a noncommutative extension of the Laplace-Varadhan asymptotic formula.
Keywords
Cite
@article{arxiv.0808.0293,
title = {A note on the non-commutative Laplace-Varadhan integral lemma},
author = {W. De Roeck and C. Maes and K. Netocny and L. Rey-Bellet},
journal= {arXiv preprint arXiv:0808.0293},
year = {2009}
}
Comments
v1-->v2, 15 pages, the conditions of the theorems have been relaxed and their proof has been simplified. The whole paper was therefore restyled. A new author is added