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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
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English version:
Theoretical and Mathematical Physics, 2011, 169:2, 1517–1529
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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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http://mi.mathnet.ru/eng/tmf6720https://doi.org/10.4213/tmf6720 http://mi.mathnet.ru/eng/tmf/v169/i2/p179
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This publication is cited in the following articles:
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Bogoliubov N.M. Malyshev C., “Correlation Functions of Xxo Heisenberg Chain, Q-Binomial Determinants, and Random Walks”, Nucl. Phys. B, 879 (2014), 268–291
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N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856
  -
J. Math. Sci. (N. Y.), 216:1 (2016), 8–22
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