Examples of DLR States Which are Not Weak Limits of Finite Volume Gibbs Measures with Deterministic Boundary Conditions

@article{Coquille2015ExamplesOD,
  title={Examples of DLR States Which are Not Weak Limits of Finite Volume Gibbs Measures with Deterministic Boundary Conditions},
  author={Loren Coquille},
  journal={Journal of Statistical Physics},
  year={2015},
  volume={159},
  pages={958-971}
}
  • Loren Coquille
  • Published 12 November 2014
  • Mathematics
  • Journal of Statistical Physics
We review what is known about the structure of the set of weak limiting states of the Ising and Potts models at low enough temperature, and in particular we prove that the mixture $$\frac{1}{2}(\mu ^\pm +\mu ^\mp )$$12(μ±+μ∓) of two reflection-symmetric Dobrushin states of the 3-dimensional Ising model at low enough temperature is a Gibbs state which is not a limit of finite-volume measures with deterministic boundary conditions. Finally we point out what the issues are in order to extend the… 

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