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Estimations of the Free Energy for the Hubbard Model

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Abstract

A series of upper bounds and two lower bounds for the partition function of the Hubbard model have been derived. These bounds are expressible by certain properties of the Falicov-Kimball model. The upper bounds have been derived mainly by the use of the Golden-Thompson inequality and its generalizations, and the Hölder inequality. The lower bounds are based on the Bogoliubov-Peierls inequality. The numerical values of bounds have also been calculated for small systems.

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Authors and Affiliations

  1. Department for Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoża 74, 00-682, Warszawa, Poland

    Jacek Wojtkiewicz

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  1. Jacek Wojtkiewicz
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Correspondence to Jacek Wojtkiewicz.

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Wojtkiewicz, J. Estimations of the Free Energy for the Hubbard Model. J Stat Phys 135, 375–387 (2009). https://doi.org/10.1007/s10955-009-9720-6

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  • DOI: https://doi.org/10.1007/s10955-009-9720-6

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