A note on the non-commutative Laplace-Varadhan integral lemma

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 [9], 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 [9], the result is a noncommutative extension of the Laplace-Varadhan asymptotic formula.

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

References in corpus (2)

• Reflection positivity and phase transitions in lattice spin models
• Large Deviations in Quantum Spin Chain