A NOTE ON THE NON-COMMUTATIVE LAPLACE–VARADHAN INTEGRAL LEMMA

Authors

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

Publication Date

2010

Journal or Book Title

Reviews in Mathematical Physics

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.

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

Pages

839-858

Volume

22

Issue

7

Recommended Citation

De Roeck, W; Maes, C; Netocny, K; and Rey-Bellet, L, "A NOTE ON THE NON-COMMUTATIVE LAPLACE–VARADHAN INTEGRAL LEMMA" (2010). Reviews in Mathematical Physics. 1175.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1175