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Berezinskii–Kosterlitz–Thouless Order in Two-Dimensional O(2)-Ferrofluid
Authors:Christian Gruber  Hiroshi Tamura  Valentin A Zagrebnov
Institution:(1) Institut de Physique Théorique, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland;(2) Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa, 920-1192, Japan;(3) Université de la Méditerranée (Aix-Marseille II) and Centre de Physique Théorique, CNRS-Luminy-Case 907, 13288 Marseille Cedex 9, France
Abstract:We study a two-dimensional ferrofluid of hard-core particles with internal degrees of freedom (plane rotators) and O(2)-invariant ferromagnetic spin interaction. By reducing the continuous system to an approximating reference lattice system, a lower bound for the two-spin correlation function is obtained. This bound, together with the Fröhlich–Spencer result about the Berezinskii–Kosterlitz–Thouless transition in the two-dimension lattice system of plane rotators, shows that our model also exhibits the same kind of ordering. Namely for a short-range ferromagnetic interaction the two-spin correlation function does not decay faster than some power of the inverse distance between particles, for small temperatures and high densities of the ferrofluid. For a long-range ferromagnetic interaction the model manifests a non-zero order parameter (magnetization) in this domain, whereas for high temperatures spin correlations decay exponentially.
Keywords:continuous systems  ferrofluids  plane rotators  Berezinskii–  Kosterlitz–  Thouless transition
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