The droplet in the tube: A case of phase transition in the canonical ensemble |
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| Authors: | S B Shlosman |
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| Institution: | 1. Centre de Physique Théorique, CNRS -- Luminy, Case 907, F-13288, Marseille Cedex 9, France
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| Abstract: | We consider the 2-dimensional Ising model with ferromagnetic nearest neighbour interaction at inverse temperature . LetS
N
= 
t
be the total magnetization inside anN×N square box ,
per
be the Gibbs state in with periodic b.c., andm() be the spontaneous magnetization. We show the existence of the limit
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![$$\psi (\varrho ) = \mathop {\lim }\limits_{N \to \infty } \left( { - \frac{1}{{\beta N}}} \right)\ln \mu _\Lambda ^{per} (S_N = N\varrho ])$$](/content/G56X0L76636169K7/220_2005_Article_BF01217770_TeX2GIFE1.gif)