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Nonextensive thermodynamics of the two-site Hubbard model

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  • Hasegawa, Hideo

Abstract

Thermodynamical properties of canonical and grand-canonical ensembles of the half-filled two-site Hubbard model have been discussed within the framework of the nonextensive statistics (NES). For relating the physical temperature T to the Lagrange multiplier β, two methods have been adopted: T=1/kBβ in method A [Tsallis et al., Physica A 261 (1998) 534], and T=cq/kBβ in method B [Abe et al., Phys. Lett. A 281 (2001) 126], where kB denotes the Boltzman constant, cq=∑ipiq,pi the probability distribution of the ith state, and q the entropic index. Temperature dependences of specific heat and magnetic susceptibility have been calculated for 1⩽q⩽2, the conventional Boltzman–Gibbs statistics being recovered in the limit of q=1. The Curie constant Γq of the susceptibility in the atomic and low-temperature limits (t/U→0,T/U→0) is shown to be given by Γq=2q22(q-1) in method A, and Γq=2q in method B, where t stands for electron hoppings and U intra-atomic interaction in the Hubbard model. These expressions for Γq are shown to agree with the results of a free spin model which have been studied also by the NES with methods A and B. A comparison has been made between the results for canonical and grand-canonical ensembles of the model.

Suggested Citation

  • Hasegawa, Hideo, 2005. "Nonextensive thermodynamics of the two-site Hubbard model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 273-293.
    • Handle: RePEc:eee:phsmap:v:351:y:2005:i:2:p:273-293
    DOI: 10.1016/j.physa.2005.01.025
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    Cited by:

    1. Balcerzak, T. & Szałowski, K., 2018. "Hubbard pair cluster in the external fields. Studies of the polarization and susceptibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1069-1084.
    2. Balcerzak, T. & Szałowski, K., 2017. "Hubbard pair cluster in the external fields. Studies of the chemical potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 252-266.
    3. Balcerzak, T. & Szałowski, K., 2018. "Hubbard pair cluster in the external fields. Studies of the magnetic properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 395-406.

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    Keywords

    Nonextensive statistics; Hubbard model;

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