A study on composed nonextensive magnetic systems

Abstract

We investigate the magnetic properties of a composed nonextensive system. The work is motivated by recent proposals that manganites are magnetically nonextensive objects, according to Tsallis statistics. We consider a two-parts composed system, A−B (both spins $\text{1}\text{2}$), and calculate self-consistently the partial magnetizations in the mean field approximation, M_A and M_B, for the cases the coupling between the subsystems is either ferro or anti-ferromagnetic. This involves the notion of partial trace in the nonextensive statistics. For temperatures below the magnetic ordering temperatures, and q≠1, we found strong disagreement between the M vs. T curves calculated from the total 4×4 Hilbert space, through ρ^q, when compared to the calculation made from the 2×2 subspaces, if we use the usual definition ρ_A(B)≡Tr_B(A)(ρ), and then elevates the matrices to the qth power, as adopted in other contexts in the literature of the nonextensive statistics. On another hand, full agreement is found if we take ρ_A(B),q≡Tr_B(A)(ρ^q), remaining q an implicit parameter.