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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| Affiliation: | 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 . LetSN=  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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![$$psi (varrho ) = mathop {lim }limits_{N to infty } left( { - frac{1}{{beta N}}} right)ln mu _Lambda ^{per} (S_N = [Nvarrho ])$$](/content/G56X0L76636169K7/220_2005_Article_BF01217770_TeX2GIFE1.gif)