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On the Aubry-Mather theory in statistical mechanics. (English) Zbl 0917.46070
Summary: We generalize Aubry-Mather theory for configurations on the line to general sets with a group action. Cocycles on the group play the role of rotation numbers. The notion of Birkhoff configuration can be generalized to this setting. Under mild conditions on the group, we show how to find Birkhoff ground states for many-body interactions which are ferromagnetic, invariant under the group action and having periodic phase space.

MSC:
46N55 Applications of functional analysis in statistical physics
82C22 Interacting particle systems in time-dependent statistical mechanics
81U10 \(n\)-body potential quantum scattering theory
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