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On the Thermodynamics of Supersymmetric Haldane–Shastry Spin Chains

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Classical and Quantum Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 229))

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Abstract

In this short report we present some recent results on the thermodynamics of \(\mathrm {su}(m|n)\) supersymmetric spin chains of Haldane–Shastry type, with long-range position-dependent interactions. We first evaluate their partition function, and then show how to express it in terms of supersymmetric Haldane motifs. This key step makes it possible to derive the thermodynamic functions of the system in closed form through a modification of the usual transfer matrix approach. In particular, from the low-temperature behavior of the free energy we obtain a full description of the critical behavior of these chains for low values of m and n.

Dedicated to our friend and colleague, Alberto Ibort, on his 60th anniversary.

Supported by MINECO (Spain) under grant FIS2015-63966-P.

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Authors and Affiliations

  1. Departamento de Física Teórica, Universidad Complutense de Madrid, 28040, Madrid, Spain

    F. Finkel, A. González-López, I. León & M. A. Rodríguez

Authors
  1. F. Finkel
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  2. A. González-López
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  3. I. León
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  4. M. A. Rodríguez
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Corresponding author

Correspondence to M. A. Rodríguez .

Editor information

Editors and Affiliations

  1. Università degli Studi di Napoli Federico II, Naples, Italy

    G. Marmo

  2. Institute of Mathematical Sciences (ICMAT), Madrid, Spain

    David Martín de Diego

  3. Universitat Politècnica de Catalunya, Barcelona, Spain

    Miguel Muñoz Lecanda

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Finkel, F., González-López, A., León, I., Rodríguez, M.A. (2019). On the Thermodynamics of Supersymmetric Haldane–Shastry Spin Chains. In: Marmo, G., Martín de Diego, D., Muñoz Lecanda, M. (eds) Classical and Quantum Physics. Springer Proceedings in Physics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-030-24748-5_10

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