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

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, 419–442 (1995)]. We complement previous results on the existence of phase transitions at low temperature [González-Navarrete et al., J. Stat. Phys. 162, 139–161 (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 [R. Dobrushin, Theory Probab. Appl. 13, 197–224 (1968)], (2) disagreement percolation [J. van den Berg and C. Maes, Ann. Probab. 22, 749–763 (1994)], and (3) Dobrushin–Shlosman criteria [R. Dobrushin and S. Shlosman, in Statistical Physics and Dynamical Systems: Rigorous Results, edited by J. Fritz, A. Jaffe, and D. Szasz (Birkhauser, Basel, 1985)]. These conditions are subsequently solved numerically and the resulting uniqueness regions are compared.