Lack of phase transitions in staggered magnetic systems. A comparison of uniqueness criteria
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 [González-Navarrete e...
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| creator | Fernández, Roberto González-Navarrete, Manuel Pechersky, Eugene Yambartsev, Anatoly |
| description | 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 [González-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. |
| doi_str_mv | 10.48550/arxiv.1901.08697 |
| format | Article |
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| subjects | Criteria Ferromagnetism Image processing Ising model Mathematical models Mathematics - Mathematical Physics Mathematics - Probability Percolation Phase transitions Physics - Mathematical Physics Uniqueness |
| title | Lack of phase transitions in staggered magnetic systems. A comparison of uniqueness criteria |
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