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van Enter, A.C.D. (author), Fukushima Kimura, B.H. (author), Ruszel, W.M. (author), Spitoni, Cristian (author)In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration - 1 is the only metastable state and we estimate the mean exit time. Moreover, we illustrate the theory with two examples (exponentially and polynomially decaying...journal article 2019
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Coquille, Loren (author), van Enter, A.C.D. (author), Le Ny, Arnaud (author), Ruszel, W.M. (author)We consider the two-dimensional Ising model with long-range pair interactions of the form (Formula presented.) with (Formula presented.), mostly when (Formula presented.). We show that Dobrushin states (i.e. extremal non-translation-invariant Gibbs states selected by mixed ± boundary conditions) do not exist. We discuss possible extensions of...journal article 2018