A study on composed nonextensive magnetic systems


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 1/2), and calculate 2 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 not equal 1, we found strong disagreement between the M vs. T curves calculated from the total 4 x 4 Hilbert space, through rho(q), when compared to the calculation made from the 2 x 2 subspaces, if we use the usual definition rho(A(B)) = Tr-B(A)(rho), 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 rho(A(B),q) = Tr-B(A)(rho(q)), remaining q an implicit parameter. (C) 2004 Elsevier B.V. All rights reserved.



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Navarro, FAR; Reis, MS; Lenzi, EK; Oliveira, IS


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