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arXiv · 1901.08697

Lack of phase transitions in staggered magnetic systems. A comparison of uniqueness criteria

Roberto Fernández·Manuel González-Navarrete·Eugene Pechersky·Anatoly Yambartsev
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Abstract

We study a ferromagnetic Ising model with a staggered cell-board magnetic field previously proposed for image processing [Maruani et al., Markov Processes Relat. Fields 1 (1995) \cite{MPS}]. We complement previous results on the existence of phase transitions at low temperature [Gonz\'alez-Navarrete et al., J. Stat. Phys. 162 (2016)] by determining bounds to the region of uniqueness of Gibbs measures. We establish sufficient rigorous uniqueness conditions derived from three different criteria: (1) Dobrushin criterion [Dobrushin, Theory Probab. Appl. 13 (1968)], (2) Disagreement percolation [van den Berg and Maes, Ann. Probab. 22 (1994)] and (3) Dobrushin-Shlosman criteria [Dobrushin and Shlosman, in Statistical Physics and Dynamical Systems. Rigorous Results. (1985)]. These conditions are subsequently solved numerically and the resulting uniqueness regions compared.

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Roberto Fernández, Manuel González-Navarrete, Eugene Pechersky, Anatoly Yambartsev. 2019-01-25. Lack of phase transitions in staggered magnetic systems. A comparison of uniqueness criteria. https://doi.org/10.1063/5.0020757

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