Nucleation for One-Dimensional Long-Range Ising Models

Aernout C.D. van Enter, Bruno Kimura, Wioletta Ruszel, Cristian Spitoni

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1 Citation (Scopus)
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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.

Original languageEnglish
Pages (from-to)1327-1345
Number of pages19
JournalJournal of Statistical Physics
Volume174
Issue number6
DOIs
Publication statusPublished - 2019

Keywords

  • Long-range Ising model
  • Metastability
  • Nucleation

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