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A discrete variational problem related to Ising droplets at low temperatures

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Abstract

We consider a variational problem on thed-dimensional latticeZ d which has applications in the study of the meatastable behavior of the stochastic Ising model. The problem, an isoperimetric one, is to find what is the smallest area a finite subset ofZ d can have restricted to three classes of subsets ofZ d. If ϕ is one of these subsets, we define its volume as the number of points in it and its area as the number of pairs of points inZ d which are neighbors and such that only one of them belongs to ϕ.

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Authors and Affiliations

  1. Instituto de Matemática e Estatistica da Universidade de São Paulo, Caixa Postal 66281, São Paulo, SP, Brazil

    E. Jordão Neves

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  1. E. Jordão Neves
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Neves, E.J. A discrete variational problem related to Ising droplets at low temperatures. J Stat Phys 80, 103–123 (1995). https://doi.org/10.1007/BF02178355

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  • DOI: https://doi.org/10.1007/BF02178355

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