Skip to main content
Article
A NOTE ON THE NON-COMMUTATIVE LAPLACE–VARADHAN INTEGRAL LEMMA
Reviews in Mathematical Physics
  • W De Roeck
  • C Maes
  • K Netocny
  • L Rey-Bellet, University of Massachusetts - Amherst
Publication Date
2010
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
Citation Information
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 Vol. 22 Iss. 7 (2010)
Available at: http://works.bepress.com/luc_rey_bellet/5/