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arXiv · 0808.0293

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

W. De Roeck·C. Maes·K. Netocny·L. Rey-Bellet
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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.

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W. De Roeck, C. Maes, K. Netocny, L. Rey-Bellet. 2009-08-29. A note on the non-commutative Laplace-Varadhan integral lemma. https://arxiv.org/abs/0808.0293

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