Abstract
We consider the calculation of the entropy of an Ising ferromagnet with nonmagnetic impurities distributed at random over the lattice sites or bonds. The Ising magnet on the Bethe lattice is analyzed. On such a lattice, the situations with a random nonmagnetic dilution over the sites and bonds are indistinguishable. For calculating the entropy, the magnetization determined in the pseudo-chaotic approximation is used. In this approximation, we obtain the entropy as a function of the temperature, the concentration of magnetic atoms, and the external magnetic field. It is found that in zero external field, the system is frustrated in the sense that the ground-state entropy differs from zero. The value of this entropy is determined for concentrations magnetic atoms below as well as above the percolation threshold.
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REFERENCES
R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, New York, 1982).
R. Fol’k, Yu. Golovach, and T. Yavorskii, Phys. Usp. 46, 169 (2003).
A. K. Murtazaev, A. B. Babaev, and G. Ya. Aznaurova, Phys. Solid State 50, 733 (2008).
S. V. Semkin and V. P. Smagin, Approximate Methods in the Theory of Pure and Dilute Magnets (VGUES, Vladivostok, 2019).
S. V. Semkin, V. P. Smagin, and E. G. Gusev, Theor. Math. Phys. 201, 1655 (2019).
S. V. Semkin and V. P. Smagin, Phys. Solid State 57, 943 (2015).
S. V. Semkin and V. P. Smagin, J. Exp. Theor. Phys. 121, 636 (2015).
I. A. Kvasnikov, Thermodynamics and Statistical Physics: Theory of Equilibrium Systems (Editorial URSS, Moscow, 2002) [in Russian].
E. S. Tsuvarev, F. A. Kassan-Ogly, and A. I. Proshkin, J. Exp. Theor. Phys. 131, 447 (2020).
Y. Shevchenko, A. Makarov, and K. Nefedev, Phys. Lett. A 381, 428 (2017).
A. V. Zarubin, F. A. Kassan-Ogly, A. I. Proshkin, and A. E. Shestakov, J. Exp. Theor. Phys. 128, 778 (2019).
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Translated by N. Wadhwa
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Semkin, S.V., Smagin, V.P. & Tarasov, V.S. Frustrations in a Diluted Ising Magnet on the Bethe Lattice. J. Exp. Theor. Phys. 134, 713–719 (2022). https://doi.org/10.1134/S1063776122060048
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DOI: https://doi.org/10.1134/S1063776122060048