On the equivalence of boundary conditions |
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Authors: | Jean Bricmont Joel L Lebowitz Charles E Pfister |
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Institution: | (1) Department of Mathematics, Rutgers University, New Brunswick, New Jersey |
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Abstract: | We show that ifb andb are two boundary conditions (b.c.) for general spin systems on
d
such that the difference in the energies of a spin configuration in
d
is uniformly bounded, |H
,b
()–H
,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research. |
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Keywords: | Boundary conditions Gibbs states spin systems |
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