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

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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.

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Authors and Affiliations

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

    N. M. Bogoliubov & C. L. Malyshev

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  1. N. M. Bogoliubov
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  2. C. L. Malyshev
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Correspondence to C. L. Malyshev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 169, No. 2, pp. 179–193, November, 2011.

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Bogoliubov, N.M., Malyshev, C.L. Ising limit of a Heisenberg XXZ magnet and some temperature correlation functions. Theor Math Phys 169, 1517–1529 (2011). https://doi.org/10.1007/s11232-011-0129-4

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