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- Title
An Ergodic Description of Ground States.
- Authors
Garibaldi, Eduardo; Thieullen, Philippe
- Abstract
Given a translation-invariant Hamiltonian $$H$$ , a ground state on the lattice $$\mathbb {Z}^d$$ 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 $$\Psi $$ defined on the space of configurations, a minimizing measure is a translation-invariant probability which minimizes the average of $$\Psi $$ . If $$\Psi _0$$ 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.
- Subjects
GROUND state energy; HAMILTONIAN mechanics; MODULES (Algebra); PROBABILITY theory; GIBBS' free energy; ERGODIC theory
- Publication
Journal of Statistical Physics, 2015, Vol 158, Issue 2, p359
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-014-1139-z