Nucleation for One-Dimensional Long-Range Ising Models
A.C.D. van Enter (Rijksuniversiteit Groningen, TU Delft - Applied Probability)
B.H. Fukushima Kimura (TU Delft - Applied Probability)
W.M. Ruszel (TU Delft - Applied Probability)
Cristian Spitoni (Universiteit Utrecht)
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Abstract
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 interaction) and we show that the critical droplet might be macroscopic or mesoscopic, according to the value of the external magnetic field.
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