Communications in Mathematical Physics

, Volume 96, Issue 1, pp 115–124 | Cite as

On solvable models in classical lattice systems

  • M. Fannes
  • A. Verbeure


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.


Neural Network Statistical Physic Equilibrium State Complex System State Space 
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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • M. Fannes
    • 1
  • A. Verbeure
    • 1
  1. 1.Instituut voor Theoretische FysicaUniversiteit LeuvenLeuvenBelgium

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