The droplet in the tube: A case of phase transition in the canonical ensemble

S. B. Shlosman

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32 Citations (Scopus)

Abstract

We consider the 2-dimensional Ising model with ferromagnetic nearest neighbour interaction at inverse temperature β. Let SN=Σσt be the total magnetization inside an N×N square box Λ, μΛper be the Gibbs state in Λ with periodic b.c., and m(β) be the spontaneous magnetization. We show the existence of the limit {Mathematical expression} for |ρ{variant}|<m(β), provided β is large enough. It turns out that the quantity ψ(ρ{variant}) is closely related to the Wulf construction, and the dependence of the function ψ(ρ{variant}) on ρ{variant} is singular.

Original languageEnglish
Pages (from-to)81-90
Number of pages10
JournalCommunications in Mathematical Physics
Volume125
Issue number1
DOIs
Publication statusPublished - Mar 1989
Externally publishedYes

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