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We build and study a multidimensional version of the Curie-Weiss model ofself-organized criticality we have designed in arXiv:1301.6911. For symmetricdistributions satisfying some integrability condition, we prove that the sum$S_n$ of the randoms vectors in the model has a typical critical behaviour. Thefluctuations are of order $n^{3/4}$ and the limiting law has a densityproportional to the exponential of a fourth-degree polynomial.

The Curie-Weiss Model of SOC in Higher Dimension