Magnetic phase diagram for a non-extensive system: Experimental connection with manganites

In the present paper we make a thorough analysis of a classical spin system, within the framework of Tsallis nonextensive statistics. From the analysis of the generalized Gibbs free energy, within the mean-field approximation, a para-ferromagnetic phase diagram, which exhibits first and second order phase transitions, is built. The features of the generalized, and classical, magnetic moment are mainly determined by the values of $q$, the non-extensive parameter. The model is successfully applied to the case of La$_{0.60}$Y$_{0.07}$Ca$_{0.33}$MnO$_3$ manganite. The temperature and magnetic field dependence of the experimental magnetization on this manganite are faithfully reproduced. The agreement between rather "exotic" magnetic properties of manganites and the predictions of the $q$-statistics, comes to support our early claim that these materials are magnetically nonextensive objects.