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 Phase Transition with the Berezinskii--Kosterlitz--Thouless Singularity in the Ising Model on a Growing Network M. Bauer ; S. Coulomb ; S.N. Dorogovtsev ; Rating: Members: 2/5 (1 reader) Date: 25 Dec 2004 Journal: Phys.Rev.Lett. 94 (2005) 200602 Subject: Statistical Mechanics; Mathematical Physics | cond-mat.stat-mech hep-lat hep-th math-ph math.MP Abstract: We consider the ferromagnetic Ising model on a highly inhomogeneous network created by a growth process. We find that the phase transition in this system is characterised by the Berezinskii--Kosterlitz--Thouless singularity, although critical fluctuations are absent, and the mean-field description is exact. Below this infinite order transition, the magnetization behaves as $exp(-const/sqrt{T_c-T})$. We show that the critical point separates the phase with the power-law distribution of the linear response to a local field and the phase where this distribution rapidly decreases. We suggest that this phase transition occurs in a wide range of cooperative models with a strong infinite-range disorder. Source: arXiv, cond-mat/0501596 Services: Forum | Review | PDF | Favorites
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 1. Science-advisor.net review 05090018 (2 readers)    Rate this comment. Review title: Magnetisation in the 2DXY model? Reviewer: Date: 23 September 2005 at 13:47 GMT. Comment: It seems that there is a problem of interpretation in this articel. There is no long range order parameter the BKT phase transition because of the Mermin-Wagner theorem at least in the 2DXY model. The magnetisation M is 0 at all temperatures for the 2DXY model. The magnetisation found in this article $M =exp(-c/(\sqrt{T_c-T})$ could be related to a 3DXY or something like that. I don't understand the BKT interpretation in this article.

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