dc.contributor.author Bru, J.-B. dc.contributor.author de Siqueira Pedra, W. dc.date.accessioned 2019-02-21T15:53:51Z dc.date.available 2019-02-21T15:53:51Z dc.date.issued 2013-07 dc.identifier.isbn 978-0-8218-8976-3 dc.identifier.uri http://hdl.handle.net/20.500.11824/938 dc.description.abstract We define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, we give a first answer to an old open problem in mathematical physics - first addressed by Ginibre in 1968 within a different context - about the validity of the so--called Bogoliubov approximation on the level of states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, our method provides a systematic way to study all its correlation functions and can thus be used to analyze the physics of long range interactions. Furthermore, we show that the thermodynamics of long range models $\mathfrak{m}\in \mathcal{M}_{1}$ is governed by the non--cooperative equilibria of a zero-sum game, called here the thermodynamic game. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Long-range en_US dc.subject Game theory en_US dc.subject Fermi systems en_US dc.subject Mean-Field en_US dc.subject Convex analysis en_US dc.subject C* algebra en_US dc.title Non-cooperative Equilibria of Fermi Systems With Long Range Interactions en_US dc.type info:eu-repo/semantics/book en_US dc.relation.publisherversion https://bookstore.ams.org/memo-224-1052 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Memoirs of the AMS en_US
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