An Ergodic Description of Ground States

Given a translation-invariant Hamiltonian H , a ground state on the lattice Z d is a configuration whose energy, calculated with respect to H , cannot be lowered by altering its states on a finite number of sites. The set formed by these configurations is translation-invariant. Given an observable Ψ...

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Bibliographic Details
Published in:Journal of statistical physics 2015-01, Vol.158 (2), p.359-371
Main Authors: Garibaldi, Eduardo, Thieullen, Philippe
Format: Article
Language:English
Subjects:
Dynamical Systems
Mathematical and Computational Physics
Mathematics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary:Given a translation-invariant Hamiltonian H , a ground state on the lattice Z d is a configuration whose energy, calculated with respect to H , cannot be lowered by altering its states on a finite number of sites. The set formed by these configurations is translation-invariant. Given an observable Ψ defined on the space of configurations, a minimizing measure is a translation-invariant probability which minimizes the average of Ψ . If Ψ 0 is the mean contribution of all interactions to the site 0 , we show that any configuration of the support of a minimizing measure is necessarily a ground state.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-014-1139-z