New Consideration on Composed Nonextensive Magnetic Systems

In this paper a composed A+B magnetic system, with spins J_A=2 and J_B=3/2, is considered within the mean-field approximation, in the framework of Tsallis nonextensive statistics. Our motivation is twofold: (1) to approach the existing experimental data of manganese oxides (manganites), where Mn^{3+...

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Bibliographic Details
Published in:arXiv.org 2009-09
Main Authors: Navarro, F A R, Reis, M S, Lenzi, E K, Olivera, I S
Format: Article
Language:English
Subjects:
Density
Entropy
Hilbert space
Internal energy
Magnetization
Manganese
Mathematical analysis
Subspaces
Subsystems
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Summary:In this paper a composed A+B magnetic system, with spins J_A=2 and J_B=3/2, is considered within the mean-field approximation, in the framework of Tsallis nonextensive statistics. Our motivation is twofold: (1) to approach the existing experimental data of manganese oxides (manganites), where Mn^{3+} and Mn^{4+} form two magnetic sublattices, and (2) to investigate the structure of nonextensive density matrices of composed systems. By imposing that thermodynamic quantities, such as the magnetization of sublattices A and B, must be invariant weather the calculation is taken over the total Hilbert space or over partial subspaces, we found that the expression for the nonextensive entropy must be adapted. Our argument is supported by calculation of sublattices magnetization M_A and M_B, internal energy, U_A and U_B, and magnetic specific heat, CA and CB. It is shown that only with the modified entropy the two methods of calculation agree to each other. Internal energy and magnetization are additive, but no clear relationship was found between S_A, S_B and the total entropy S_{A+B} for q \neq 1. It is shown that the reason for the failure of the standard way of calculation is the assumption of statistical independence between the two subsystems, which however does not affect the density matrix in the full Hilbert space.
ISSN:2331-8422