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Correlation Identities, Correlation Inequalities, and Upper Bounds on Critical Temperature of Spin Systems

  • Condensed Matter
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Abstract

A review on spin correlation functions identities and on rigorous correlation functions inequalities is presented for various spin models. The spin correlation identities are exactly obtained from finite cluster of spins for different models, and the rigorous spin correlation inequalities are presented for the discrete and continuous classical spin models and also for quantum spin models. Through these correlation identities and rigorous inequalities, the upper bounds on critical temperatures are obtained by the decay of the correlation function.

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Notes

  1. Remarck:the coefficients A s i , where s stands for the subsection, appearing along the next five subsections, have a different notation in the cited papers.

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Acknowledgments

JPS financial support from FAPEMIG/Brazil. FCSB is grateful to CAPES/Brazil for the financial support that made possible his visit to the UFSJ/Brazil.

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Authors and Affiliations

  1. Departamento de Ciências Naturais, Universidade Federal de São João del Rei, C.P. 110, CEP 36301-160, São João del Rei, Brazil

    J. P. Santos & F. C. Sá Barreto

  2. Departamento de Física, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte, MG, Brazil

    F. C. Sá Barreto

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  1. J. P. Santos
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Correspondence to J. P. Santos.

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Santos, J.P., Sá Barreto, F.C. Correlation Identities, Correlation Inequalities, and Upper Bounds on Critical Temperature of Spin Systems. Braz J Phys 45, 147–165 (2015). https://doi.org/10.1007/s13538-014-0275-x

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