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Decorated Ising Chain in a Magnetic Field

  • ORDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
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Abstract

The Kramers–Wannier transfer matrix method is generalized to an arbitrary decoration number of the Ising chain. An exact analytical expression is obtained for the largest eigenvalue of the transfer matrix of a decorated Ising chain in the presence of an external magnetic field. Frustration points and the values of frustration magnetic fields are found that depend on the magnitudes and signs of exchange interactions. Exact expressions are obtained for zero-temperature entropies and zero-temperature magnetizations of the model under consideration. Magnetic phase diagrams of the ground state of the system are constructed for decoration values of d = 1 and d = 2, including those in the absence of a magnetic field. A comparison is made with a decorated square lattice not only in the absence but also in the presence of a magnetic field.

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Funding

This work was supported by the Ministry of Education and Science of the Russian Federation within the state assignment (projects “Kvant,” no. AAAA-A18-118020190095-4, and “Splavy,” no. AAAA-A19-119070890020-3) and in part by the Ural Branch of the Russian Academy of Sciences (project no. 18-2-2-11).

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Authors and Affiliations

  1. Ural Federal University Named after the First President of Russia B.N. Yeltsin, 620000, Yekaterinburg, Russia

    E. S. Tsuvarev

  2. Mikheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, 620108, Yekaterinburg, Russia

    E. S. Tsuvarev & F. A. Kassan-Ogly

Authors
  1. E. S. Tsuvarev
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  2. F. A. Kassan-Ogly
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Correspondence to E. S. Tsuvarev or F. A. Kassan-Ogly.

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Translated by I. Nikitin

APPENDIX

APPENDIX

To take the integral in (32), we apply the following formula [23]:

$$\int\limits_0^\pi {\ln (a + b\cos \phi )d\phi = \pi \ln \frac{{a + \sqrt {{{a}^{2}} - {{b}^{2}}} }}{2}.} $$
(A.1)

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Tsuvarev, E.S., Kassan-Ogly, F.A. Decorated Ising Chain in a Magnetic Field. J. Exp. Theor. Phys. 131, 976–987 (2020). https://doi.org/10.1134/S1063776120120122

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  • DOI: https://doi.org/10.1134/S1063776120120122

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