Abstract
We consider one dimensional classical lattice systems and an increasing sequence ℒ n (n=1,2, ...) of subsets of the state space; ℒ n takes into account correlations betweenn successive lattice points.
If the interaction range of the potential is finite, we prove that the equilibrium states defined by the variational principle are elements of {ℒ n } n<∞. Finally we give a new proof of the fact that all faithful states of ℒ n are DLR-states for some potential.
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Communicated by H. Araki
Bevoegdverklaard navorser NFWO
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Fannes, M., Verbeure, A. On solvable models in classical lattice systems. Commun.Math. Phys. 96, 115–124 (1984). https://doi.org/10.1007/BF01217350
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DOI: https://doi.org/10.1007/BF01217350