Communications in Mathematical Physics

, Volume 125, Issue 1, pp 81–90 | Cite as

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

  • S. B. Shlosman


We consider the 2-dimensional Ising model with ferromagnetic nearest neighbour interaction at inverse temperatureβ. LetS N σ t be the total magnetization inside anN×N square boxΛ,μ Λ per be the Gibbs state inΛ with periodic b.c., andm(β) be the spontaneous magnetization. We show the existence of the limit
$$\psi (\varrho ) = \mathop {\lim }\limits_{N \to \infty } \left( { - \frac{1}{{\beta N}}} \right)\ln \mu _\Lambda ^{per} (S_N = [N\varrho ])$$
for |ϱ|<m(β), providedβ is large enough. It turns out that the quantityψ(ϱ) is closely related to the Wulf construction, and the dependence of the functionψ(ϱ) onϱ is singular.


Neural Network Phase Transition Statistical Physic Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • S. B. Shlosman
    • 1
  1. 1.Centre de Physique ThéoriqueCNRS -- Luminy, Case 907Marseille Cedex 9France

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