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Residual entropy of spin-s triangular Ising antiferromagnet

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Abstract

We employ a thermodynamic integration method (TIM) to establish the values of the residual entropy for the geometrically frustrated spin-s triangular Ising antiferromagnet, with the spin values s = 1/2, 1, 3/2, 2 and 5/2. The case of s = 1/2, for which the exact value is known, is used to assess the TIM performance. We also obtain an analytical formula for the lower bound in a general spin-s model and conjecture that it should reasonably approximate the true residual entropy for sufficiently large s. Implications of the present results in relation to reliability of the TIM as an indirect method for calculating global thermodynamic quantities, such as the free energy and the entropy, in similar systems involving frustration and/or higher spin values by standard Monte Carlo sampling are briefly discussed.

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References

  1. R. Liebmann, Statistical Mechanics of Periodic Frustrated Ising Systems (Springer-Verlag, Berlin, 1986)

  2. B. Simon, The Statistical Mechanics of Lattice Gases 1 (Princeton University Press, Princeton, 1993)

  3. R. Moessner, S.L. Sondhi, Phys. Rev. B 63, 224401 (2001)

    Article  ADS  Google Scholar 

  4. G.H. Wannier, Phys. Rev. 79, 357 (1950)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. G.H. Wannier, Phys. Rev. B 7, 5017 (1973)

    Article  ADS  Google Scholar 

  6. R.M.F. Houtappel, Physica 16, 425 (1950)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. K. Husimi, I. Shozi, Prog. Theor. Phys. 5, 177 (1950)

    Article  ADS  Google Scholar 

  8. K. Husimi, I. Shozi, Prog. Theor. Phys. 5, 341 (1950)

    ADS  Google Scholar 

  9. O. Nagai, S. Miyashita, T. Horiguchi, Phys. Rev. B 47, 202 (1993)

    Article  ADS  Google Scholar 

  10. Y. Yamada, S. Miyashita, T. Horiguchi, M. Kang, O. Nagai, J. Magn. Magn. Mater. 140-144, 1749 (1995)

    Article  ADS  Google Scholar 

  11. A. Lipowski, T. Horiguchi, D. Lipowska, Phys. Rev. Lett. 74, 3888 (1995)

    Article  ADS  Google Scholar 

  12. C. Zeng, C.L. Henley, Phys. Rev. B 55, 14935 (1997)

    Article  ADS  Google Scholar 

  13. S. Kirkpatrick, Phys. Rev. B 16, 4630 (1977)

    Article  ADS  Google Scholar 

  14. J. Vannimenus, G. Toulouse, J. Phys. C 10, L537 (1977)

    Article  ADS  Google Scholar 

  15. I. Morgenstern, K. Binder, Phys. Rev. B 22, 288 (1980)

    Article  ADS  Google Scholar 

  16. H.-F. Cheung, W.L. McMillan, J. Phys. C 16, 7027 (1983)

    Article  ADS  Google Scholar 

  17. A.J. Kolan, R.G. Palmer, J. Appl. Phys. 53, 2198 (1982)

    Article  ADS  Google Scholar 

  18. A.K. Hartmann, Phys. Rev. E 63, 016106 (2001)

    Article  ADS  Google Scholar 

  19. F. Romá, F. Nieto, E.E. Vogel, A.J. Ramirez-Pastor, J. Stat. Phys. 114, 1325 (2004)

    Article  ADS  MATH  Google Scholar 

  20. K. Binder, J. Comput. Phys. 59, 1 (1985)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. H. Theil, Economic Forecasts and Policy XV (North-Holland Pub. Co., Amsterdam, 1961)

  22. M.E. Zhitomirsky, Phys. Rev. B 67, 104421 (2003)

    Article  ADS  Google Scholar 

  23. K. Binder, Rep. Prog. Phys. 50, 783 (1987)

    Article  ADS  Google Scholar 

  24. F. Wang, D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001)

    Article  ADS  Google Scholar 

  25. J.A. Plascak, A.M. Ferrenberg, D.P. Landau, Phys. Rev. E 65, 066702 (2002)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 04154, Košice, Slovakia

    Milan Žukovič

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  1. Milan Žukovič
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Correspondence to Milan Žukovič.

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Žukovič, M. Residual entropy of spin-s triangular Ising antiferromagnet. Eur. Phys. J. B 86, 283 (2013). https://doi.org/10.1140/epjb/e2013-40439-x

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