In arXiv:1301.6911, we built and studied a Curie-Weiss model exhibiting self-organized criticality : it is a model with a self-interaction leading to fluctuations of order $n^{ 3/4}$ and a limiting law proportional to $\exp(-x^4/12)$. In this paper we modify our model in order to "kill the term $x^4$" and to obtain a self-interaction leading to fluctuations of order $n^{ 5/6}$ and a limiting law $C\,\exp(-\lambda x^6)\,dx$, for suitable positive constants $C$ and $\lambda$.
Categories: math.PR math-ph math.MP