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Thermodynamics of the classical spin-ice model with nearest neighbour interactions using the Wang-Landau algorithm

  • Maria V. Ferreyra
  • Gaston Giordano
  • Rodolfo A. Borzi
  • Joseph J. Betouras
  • Santiago A. Grigera
Open Access
Regular Article

Abstract

In this article we study the classical nearest-neighbour spin-ice model (nnSI) by means of Monte Carlo simulations, using the Wang-Landau algorithm. The nnSI describes several of the salient features of the spin-ice materials. Despite its simplicity it exhibits a remarkably rich behaviour. The model has been studied using a variety of techniques, thus it serves as an ideal benchmark to test the capabilities of the Wang Landau algorithm in magnetically frustrated systems. We study in detail the residual entropy of the nnSI and, by introducing an applied magnetic field in two different crystallographic directions ([111] and [100]), we explore the physics of the kagome-ice phase, the transition to full polarisation, and the three dimensional Kasteleyn transition. In the latter case, we discuss how additional constraints can be added to the Hamiltonian, by taking into account a selective choice of states in the partition function and, then, show how this choice leads to the realization of the ideal Kasteleyn transition in the system.

Keywords

Solid State and Materials 

References

  1. 1.
    A.P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994) CrossRefADSGoogle Scholar
  2. 2.
    R. Moessner, Can. J. Phys. 79, 1283 (2001) CrossRefADSGoogle Scholar
  3. 3.
    C. Lacroix, P. Mendels, F. Mila, in Introduction to Frustrated Magnetism: Materials, Experiments, Theory (Springer Science & Business Media, 2011), Vol. 164 Google Scholar
  4. 4.
    F. Wang, D.P. Landau, Phys. Rev. Lett. 86, 2050 (2001) CrossRefADSGoogle Scholar
  5. 5.
    F. Wang, D.P. Landau, Phys. Rev. E 64, 056101 (2001) CrossRefADSGoogle Scholar
  6. 6.
    W. Lin, T. Yang, Y. Wang, M. Qin, J.-M. Liu, Z. Ren, Phys. Lett. A 378, 2565 (2014) CrossRefADSMATHGoogle Scholar
  7. 7.
    V.T. Ngo, H.T. Diep, Phys. Rev. E 78, 031119 (2008) CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    S. Papanikolaou, J.J. Betouras, Phys. Rev. Lett. 104, 045701 (2010) CrossRefADSGoogle Scholar
  9. 9.
    B.C. den Hertog, M.J.P. Gingras, Phys. Rev. Lett. 84, 3430 (2000) CrossRefADSGoogle Scholar
  10. 10.
    S.V. Isakov, K.S. Raman, R. Moessner, S.L. Sondhi, Phys. Rev. B 70, 104418 (2004) CrossRefADSGoogle Scholar
  11. 11.
    R. Moessner, S.L. Sondhi, Phys. Rev. B 68, 064411 (2003) CrossRefADSGoogle Scholar
  12. 12.
    L.D.C. Jaubert, J.T. Chalker, P.C.W. Holdsworth, R. Moessner, Phys. Rev. Lett. 100, 067207 (2008) CrossRefADSGoogle Scholar
  13. 13.
    L.D.C. Jaubert, J.T. Chalker, P.C.W. Holdsworth, R. Moessner, J. Phys.: Conf. Ser. 145, 012024 (2009) ADSGoogle Scholar
  14. 14.
    G. Torrie, J. Valleau, J. Comput. Phys. 23, 187 (1977) CrossRefADSGoogle Scholar
  15. 15.
    B.A. Berg, T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992) CrossRefADSGoogle Scholar
  16. 16.
    R.E. Belardinelli, V.D. Pereyra, Phys. Rev. E 75, 046701 (2007) CrossRefADSGoogle Scholar
  17. 17.
    S. Bramwell, M. Gingras, P. Holdsworth, H. Diep, in Frustrated Spin Systems, edited by HT Diep (World Scientific, 2004) Google Scholar
  18. 18.
    S.T. Bramwell, M.J.P. Gingras, Science 294, 1495 (2001) CrossRefADSGoogle Scholar
  19. 19.
    J.D. Bernal, R.H. Fowler, J. Chem. Phys. 1, 515 (1933) CrossRefADSGoogle Scholar
  20. 20.
    A.P. Ramirez, A. Hayashi, R. Cava, R. Siddharthan, B. Shastry, Nature 399, 333 (1999) CrossRefADSGoogle Scholar
  21. 21.
    R.G. Melko, M.J.P. Gingras, J. Phys.: Condens. Matter 16, R1277 (2004) ADSGoogle Scholar
  22. 22.
    D. Pomaranski, L. Yaraskavitch, S. Meng, K. Ross, H. Noad, H. Dabkowska, B. Gaulin, J. Kycia, Nat. Phys. 9, 353 (2013) CrossRefGoogle Scholar
  23. 23.
    L. Pauling, J. Am. Chem. Soc. 57, 2680 (1935) CrossRefGoogle Scholar
  24. 24.
    V.F. Petrenko, R.W. Whitworth, Physics of Ice (Oxford University Press, 1999) Google Scholar
  25. 25.
    E.H. Lieb, Phys. Rev. 162, 162 (1967) CrossRefADSGoogle Scholar
  26. 26.
    J.F. Nagle, J. Math. Phys. 7, 1484 (1966) CrossRefADSMathSciNetGoogle Scholar
  27. 27.
    E.A. DiMarzio, F.H. Stillinger, J. Chem. Phys. 40, 1577 (1964) CrossRefADSGoogle Scholar
  28. 28.
    R.R. Singh, J. Oitmaa, Phys. Rev. B 85, 144414 (2012) CrossRefADSGoogle Scholar
  29. 29.
    B.A. Berg, C. Muguruma, Y. Okamoto, Phys. Rev. B 75, 092202 (2007) CrossRefADSGoogle Scholar
  30. 30.
    B.A. Berg, T. Celik, Phys. Rev. Lett. 69, 2292 (1992) CrossRefADSGoogle Scholar
  31. 31.
    C. Castelnovo, R. Moessner, S.L. Sondhi, Nature 451, 42 (2008) CrossRefADSGoogle Scholar
  32. 32.
    M. Udagawa, M. Ogata, Z. Hiroi, J. Phys. Soc. Jpn 71, 2365 (2002) CrossRefADSGoogle Scholar
  33. 33.
    A. Wills, R. Ballou, C. Lacroix, Phys. Rev. B 66, 144407 (2002) CrossRefADSGoogle Scholar
  34. 34.
    P.W. Kasteleyn, J. Math. Phys. 4, 287 (1963) CrossRefADSMathSciNetGoogle Scholar
  35. 35.
    J. Nagle, Proc. Natl. Acad. Sci. USA 70, 3443 (1973) CrossRefADSGoogle Scholar
  36. 36.
    J. Nagle, Phys. Rev. Lett. 34, 1150 (1975) CrossRefADSGoogle Scholar
  37. 37.
    J.F. Nagle, C.S. Yokoi, S.M. Bhattacharjee, Phase Transitions 13, 236 (1989) Google Scholar
  38. 38.
    L.D. Jaubert, J. Chalker, P. Holdsworth, R. Moessner, J. Phys.: Conf. Ser. 145, 012024 (2009) ADSGoogle Scholar
  39. 39.
    L.D. Jaubert, Topological Constraints and Defects in Spin Ice, Ph.D. Thesis, ENS Lyon, 2009 Google Scholar

Copyright information

© The Author(s) 2016

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Maria V. Ferreyra
    • 1
    • 2
  • Gaston Giordano
    • 3
  • Rodolfo A. Borzi
    • 1
  • Joseph J. Betouras
    • 4
  • Santiago A. Grigera
    • 1
    • 5
  1. 1.Instituto de Física de Líquidos y Sistemas Biológicos (IFLySIB), UNLP-CONICETLa PlataArgentina
  2. 2.Facultad de Ciencias Exactas y Naturales, Universidad Nacional de La PampaSanta RosaArgentina
  3. 3.Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La PlataLa PlataArgentina
  4. 4.Department of PhysicsLoughborough UniversityLoughboroughUK
  5. 5.School of Physics and Astronomy, University of St Andrews,St AndrewsUK

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