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TMF, 2011, Volume 169, Number 2, Pages 179–193 (Mi tmf6720)  

This article is cited in 3 scientific papers (total in 3 papers)

Ising limit of a Heisenberg $XXZ$ magnet and some temperature correlation functions

N. M. Bogolyubov, K. L. Malyshev

St. Petersburg Department of the Steklov Institute of Mathematics, RAS, St. Petersburg, Russia

Abstract: We consider the Heisenberg spin-$1/2$ $XXZ$ magnet in the case where the anisotropy parameter tends to infinity (the so-called Ising limit). We find the temperature correlation function of a ferromagnetic string above the ground state. Our approach to calculating correlation functions is based on expressing the wave function in the considered limit in terms of Schur symmetric functions. We show that the asymptotic amplitude of the above correlation function at low temperatures is proportional to the squared number of strict plane partitions in a box.

Keywords: Heisenberg magnet, Ising limit, correlation function

DOI: https://doi.org/10.4213/tmf6720

Full text: PDF file (581 kB)
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English version:
Theoretical and Mathematical Physics, 2011, 169:2, 1517–1529

Bibliographic databases:

Document Type: Article

Citation: N. M. Bogolyubov, K. L. Malyshev, “Ising limit of a Heisenberg $XXZ$ magnet and some temperature correlation functions”, TMF, 169:2 (2011), 179–193; Theoret. and Math. Phys., 169:2 (2011), 1517–1529

Citation in format AMSBIB
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\pages 179--193
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  • https://doi.org/10.4213/tmf6720
  • http://mi.mathnet.ru/eng/tmf/v169/i2/p179

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bogoliubov N.M. Malyshev C., “Correlation Functions of Xxo Heisenberg Chain, Q-Binomial Determinants, and Random Walks”, Nucl. Phys. B, 879 (2014), 268–291  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. J. Math. Sci. (N. Y.), 216:1 (2016), 8–22  mathnet  crossref  mathscinet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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