Non-Extensivity of Inhomogeneous Magnetic Systems

In recent publications we developed the main features of a generalized magnetic system, in the sense of the non-extensive Tsallis thermostatistics. Our mean-field-non-extensive models predict phase transitions of first and second order, as well as various magnetic anomalies, as a direct consequence of non-extensivity. These theoretical features are in agreement with the unusual magnetic properties of manganites, materials which are intrinsically inhomogeneous. In the present work, we consider an inhomogeneous magnetic system composed by many homogeneous subsystems, and show that applying the usual Maxwell-Boltzmann statistics to each homogeneous bit and averaging over the whole system is equivalent of using the non-extensive approach. An analytical expression for the Tsallis entropic parameter q was obtained, and showed to be related to the moments of the distribution of the inhomogeneous quantity. Finally, it is shown that the description of manganites using Griffiths phase can be recovered with the use of the non-extensive formalism.