A note on the non-commutative laplace-varadhan integral lemma
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 Hia...
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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2010
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| In: |
Reviews in mathematical physics
Year: 2010, Volume: 22, Issue: 7, Pages: 839-858 |
| ISSN: | 1793-6659 |
| DOI: | 10.1142/S0129055X10004089 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1142/S0129055X10004089 Verlag, lizenzpflichtig, Volltext: https://www.worldscientific.com/doi/abs/10.1142/S0129055X10004089 
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| Author Notes: | W. De Roeck, Christian Maes, Karel Netočný, Luc Rey-Bellet |
| Summary: | 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. |
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| Item Description: | Gesehen am 15.09.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1793-6659 |
| DOI: | 10.1142/S0129055X10004089 |