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.
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Gruber, C., Tamura, H. & Zagrebnov, V.A. Berezinskii–Kosterlitz–Thouless Order in Two-Dimensional O(2)-Ferrofluid. Journal of Statistical Physics 106, 875–893 (2002). https://doi.org/10.1023/A:1014021400408
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DOI: https://doi.org/10.1023/A:1014021400408