On the Aubry–Mather Theory in Statistical Mechanics |
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| Authors: | A Candel R de la Llave |
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| Institution: | (1) Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA , US;(2) Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA, US |
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| Abstract: | 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.
Received: 15 May 1996 / Accepted: 22 July 1997 |
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