Abstract
The important properties of the Ising antiferromagnets on honeycomb lattice and square lattice in the critical magnetic field B c (B c = 3|J| for honeycomb lattice and B c = 4|J| for square lattice with coupling constant J) are investigated by evaluating exactly all their possible ground states on L × 2L honeycomb lattices (L = 4 ∼ 14) and L × L square lattices (L = 4 ∼ 16) with cylindrical boundary conditions. In particular, the properties of the honeycomb-lattice Ising antiferromagnet in the critical magnetic field B c are unveiled for the first time.
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References
L. Onsager, Phys. Rev. 65, 117 (1944).
C. N. Yang, Phys. Rev. 85, 808 (1952).
C. Domb, The Critical Point (Taylor and Francis, London, 1996).
B. D. Metcalf and C. P. Yang, Phys. Rev. B 18, 2304 (1978).
M. Kaufman, Phys. Rev. B 36, 3697 (1987).
S. Milosevic, B. Stosic and T. Stosic, Physica A 157, 899 (1989).
F. Y. Wu, X. N. Wu and H. W. J. Blöte,, Phys. Rev. Lett. 62, 2773 (1989).
X. N. Wu and F. Y. Wu, Phys. Lett. A 144, 123 (1990).
X. -Z. Wang and J. S. Kim, Phys. Rev. Lett. 78, 413 (1997).
J. L. Monroe, Phys. Rev. E 64, 016126 (2001).
S. -Y. Kim, Phys. Rev. Lett. 93, 130604 (2004).
S. -Y. Kim, C.-O. Hwang and J. M. Kim, Nucl. Phys. B 805, 441 (2008).
I. C. Dinola, A. Saguia and B. Boechat, Phys. Lett. A 373, 1606 (2009).
X. Yao, Solid State Commun. 150, 160 (2010).
S. -Y. Kim, Phys. Rev. E 82, 041107 (2010).
S. L. A. de Queiroz, Phys. Rev. E 84, 031132 (2011).
M. Matsuda, M. Azuma, M. Tokunaga, Y. Shimakawa and N. Kumada, Phys. Rev. Lett. 105, 187201 (2010).
K. Katsumata, H. A. Katori, S. Kimura, Y. Narumi, M. Hagiwara and K. Kindo, Phys. Rev. B 82, 104402 (2010).
S. Matas, E. Dudzik, R. Feyerherm, S. Gerischer, S. Klemke, K. Prokes and A. Orendacova, Phys. Rev. B 82, 184427 (2010).
M. Fujihala, X. G. Zheng, Y. Oohara, H. Morodomi, T. Kawae, A. Matsuo and K. Kindo, Phys. Rev. B 85, 012402 (2012).
W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, Numerical Recipes in Fortran 77, 2nd ed. (Cambridge University Press, Cambridge, 1992), p. 104.
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Kim, SY. Ising antiferromagnets on honeycomb and square lattices in the critical magnetic field. Journal of the Korean Physical Society 61, 1950–1955 (2012). https://doi.org/10.3938/jkps.61.1950
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DOI: https://doi.org/10.3938/jkps.61.1950