MPEJ Volume 11, No. 4, 27 pp. Received: Mar 11, 2004. Revised: Sep 18, 2005. Accepted: Oct 14, 2005. O. Garet Central limit theorems for the Potts Model ABSTRACT: We prove various $q$-dimensional Central Limit Theorems for the occuring of the states in the $q$-state Potts model on $\Zd$ at inverse temperature $\beta$, provided that $\beta$ is sufficiently far from the critical point $\beta_c$. When $(d=2)$ and ($q=2$ or $q\ge 26$), the theorems apply for each $\beta\ne\beta_c$. In the uniqueness region, a classical Gaussian limit is obtained. In the phase transition regime, the situation is more complex: when $(q\ge 3)$, the limit may be Gaussian or not, depending on the Gibbs measure which is considered. Particularly, we show that free boundary conditions lead to a non-Gaussian limit. Some particular properties of the Ising model are also discussed. The limits that are obtained are identified relatively to FK-percolation models. http://www.maia.ub.es/mpej/Vol/11/4.ps http://www.maia.ub.es/mpej/Vol/11/4.pdf http://www.ma.utexas.edu/mpej/Vol/11/4.ps http://www.ma.utexas.edu/mpej/Vol/11/4.pdf http://mpej.unige.ch/mpej/Vol/11/4.ps http://mpej.unige.ch/mpej/Vol/11/4.pdf