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First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited

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Abstract

We investigate the first-order transition in the spin-1 two-dimensional Blume-Capel model in square lattices by revisiting the transfer-matrix method. With large strip widths increased up to the size of 18 sites, we construct the detailed phase coexistence curve which shows excellent quantitative agreement with the recent advanced Monte Carlo results. In the deep first-order area, we observe the exponential system-size scaling of the spectral gap of the transfer matrix from which linearly increasing interfacial tension is deduced with decreasing temperature. We find that the first-order signature at low temperatures is strongly pronounced with much suppressed finite-size influence in the examined thermodynamic properties of entropy, non-zero spin population, and specific heat. It turns out that the jump at the transition becomes increasingly sharp as it goes deep into the first-order area, which is in contrast to the Wang–Landau results where finite-size smoothing gets more severe at lower temperatures.

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References

  1. M. Blume, Phys. Rev. 141, 517 (1966)

    Article  ADS  Google Scholar 

  2. H.W. Capel, Physica (Utr.) 32, 966 (1966)

    Article  ADS  Google Scholar 

  3. H.W. Capel, Physica (Utr.) 33, 295 (1967)

    Article  ADS  Google Scholar 

  4. H.W. Capel, Physica (Utr.) 37, 423 (1967)

    Article  ADS  Google Scholar 

  5. I.D. Lawrie, S. Sarbach, in Phase transitions and critical phenomena, edited by C. Domb, J.L. Lebowitz (Academic, London, 1984), Vol. 9

  6. N. Farahmand Bafi, A. Maciołek, S. Dietrich, Phys. Rev. E 91, 022138 (2015)

    Article  ADS  Google Scholar 

  7. Y. Shin, C.H. Schunck, A. Schirotzek, W. Ketterle, Nature (London) 451, 689 (2008)

    Article  ADS  Google Scholar 

  8. P.D. Beale, Phys. Rev. B 33, 1717 (1986)

    Article  ADS  Google Scholar 

  9. J.C. Xavier, F.C. Alcaraz, D. Pena Lara, J.A. Plascak, Phys. Rev. B 57, 11575 (1998)

    Article  ADS  Google Scholar 

  10. D.P. Landau, R.H. Swendsen, Phys. Rev. Lett. 46, 1437 (1981)

    Article  ADS  Google Scholar 

  11. D.P. Landau, R.H. Swendsen, Phys. Rev. B 33, 7700 (1986)

    Article  ADS  Google Scholar 

  12. N.B. Wilding, P. Nielaba, Phys. Rev. E 53, 926 (1996)

    Article  ADS  Google Scholar 

  13. J.A. Plascak, P.H.L. Martins, Comput. Phys. Commun. 184, 259 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  14. C.J. Silva, A.A. Caparica, J.A. Plascak, Phys. Rev. E 73, 036702 (2006)

    Article  ADS  Google Scholar 

  15. D. Hurt, M. Eitzel, R. Scalettar, G. Batrouni, in Computer simulation studies in condensed-matter physics XVIII, edited by D.P. Landau, S.P. Lewis, H.-B. Schuttler (Springer-Verlag, Berlin, 2007), p. 101

  16. A. Malakis, A.N. Berker, I.A. Hadjiagapiou, N.G. Fytas, Phys. Rev. E 79, 011125 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  17. A. Malakis, A.N. Berker, I.A. Hadjiagapiou, N.G. Fytas, T. Papakonstantinou, Phys. Rev. E 81, 041113 (2010)

    Article  ADS  Google Scholar 

  18. N. Fytas, Eur. Phys. J. B 79, 21 (2011)

    Article  ADS  Google Scholar 

  19. W. Kwak, J. Jeong, J. Lee, D.-H. Kim, Phys. Rev. E 92, 022134 (2015)

    Article  ADS  Google Scholar 

  20. A. Valentim, C.J. DaSilva, C.E. Fiore, Comput. Phys. Commun. 196, 212 (2015)

    Article  ADS  Google Scholar 

  21. L.-P. Yang, Z.-Y. Xie, J. Phys. Soc. Jpn. 85, 104602 (2016)

    Article  ADS  Google Scholar 

  22. K. Kimura, S. Higuchi, J. Stat. Mech. 2016, 123207 (2016)

    Article  Google Scholar 

  23. J. Zierenberg, N.G. Fytas, M. Weigel, W. Janke, A. Malakis, Eur. Phys. J. Spec. Top. 226, 789 (2017)

    Article  Google Scholar 

  24. A. Malakis, A.N. Berker, N.G. Fytas, T. Papakonstantinou, Phys. Rev. E 85, 061106 (2012)

    Article  ADS  Google Scholar 

  25. P.E. Theodorakis, N.G. Fytas, Phys. Rev. E 86, 011140 (2012)

    Article  ADS  Google Scholar 

  26. N.G. Fytas, P.E. Theodorakis, Eur. Phys. J. B 86, 30 (2013)

    Article  ADS  Google Scholar 

  27. F.P. Fernandes, F.W.S. Lima, J.A. Plascak, Comput. Phys. Commun. 181, 1218 (2010)

    Article  ADS  Google Scholar 

  28. F.P. Fernandes, D.F. de Albuquerque, F.W.S. Lima, J.A. Plascak, Phys. Rev. E 92, 022144 (2015)

    Article  ADS  Google Scholar 

  29. R. Erichsen, Jr. A.A. Lopes, S.G. Magalhaes, Phys. Rev. E 95, 062113 (2017)

    Article  ADS  Google Scholar 

  30. M.P.M. den Nijs, J. Phys. A: Math. Gen. 12, 1857 (1979)

    Article  ADS  Google Scholar 

  31. B. Nienhuis, A.N. Berker, E.K. Riedel, M. Schick, Phys. Rev. Lett. 43, 737 (1979)

    Article  ADS  Google Scholar 

  32. R.B. Pearson, Phys. Rev. B 22, 2579 (1980)

    Article  ADS  Google Scholar 

  33. B. Nienhuis, J. Phys. A: Math. Gen. 15, 199 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  34. W. Hu, R.R.P. Singh, R.T. Scalettar, Phys. Rev. E 95, 062122 (2017)

    Article  ADS  Google Scholar 

  35. B.A. Berg, T. Neuhaus, Phys. Lett. B 267, 249 (1991)

    Article  ADS  Google Scholar 

  36. B.A. Berg, T. Neuhaus, Phys. Rev. Lett. 68, 9 (1992)

    Article  ADS  Google Scholar 

  37. W. Janke, Int. J. Mod. Phys. C 03, 1137 (1992)

    Article  ADS  Google Scholar 

  38. W. Janke, Physica A 254, 164 (1998)

    Article  ADS  Google Scholar 

  39. J. Zierenberg, N.G. Fytas, W. Janke, Phys. Rev. E 91, 032126 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  41. F. Wang, D.P. Landau, Phys. Rev. E 64, 056101 (2001)

    Article  ADS  Google Scholar 

  42. C.E. Fiore, Phys. Rev. E 78, 041109 (2008)

    Article  ADS  Google Scholar 

  43. C.E. Fiore, M.G.E. da Luz, Phys. Rev. Lett. 107, 230601 (2011)

    Article  ADS  Google Scholar 

  44. C. Domb, Adv. Phys. 9, 149 (1960)

    Article  ADS  Google Scholar 

  45. J.M. Thijssen, Computational physics (Cambridge University Press, Cambridge, 2007), pp. 343–347

  46. P.A. Rikvold, W. Kinzel, J.D. Gunton, K. Kaski, Phys. Rev. B 28, 2686 (1983)

    Article  ADS  Google Scholar 

  47. B. Derrida, H.J. Herrmann, J. Phys. France 44, 1365 (1983)

    Article  Google Scholar 

  48. H.J. Herrmann, Phys. Lett. A 100, 256 (1984)

    Article  ADS  Google Scholar 

  49. P.D. Beale, J. Phys. A: Math. Gen. 17, L335 (1984)

    Article  ADS  Google Scholar 

  50. N.C. Bartelt, T.L. Einstein, L.D. Roelofs, Phys. Rev. B 34, 1616 (1986)

    Article  ADS  Google Scholar 

  51. K. Wu, H. Simon, SIAM J. Matrix Anal. Appl. 22, 602 (2000)

    Article  MathSciNet  Google Scholar 

  52. K. Wu, A. Canning, H.D. Simon, L.-W. Wang, J. Comput. Phys. 154, 156 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  53. V. Privman, M.E.J. Fisher, J. Stat. Phys. 33, 385 (1983)

    Article  ADS  Google Scholar 

  54. B. Derrida, L. De Seze, J. Phys. France 43, 475 (1982)

    Article  Google Scholar 

  55. H.W.J. Blöte, M.P. Nightingale, Physica A 112, 405 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  56. M.N. Barber, in Phase transitions and critical phenomena, edited by C. Domb, J. Lebowitz (Academic, London, 1983), Vol. 8

  57. V. Privman, M.E. Fisher, J. Phys. A: Math. Gen. 16, L295 (1983)

    Article  ADS  Google Scholar 

  58. H.J. Herrmann, D. Stauffer, Phys. Lett. A 100, 366 (1984)

    Article  ADS  Google Scholar 

  59. J.M. Luck, Phys. Rev. B 31, 3069 (1985)

    Article  ADS  Google Scholar 

  60. H.W.J. Blöte, M.P.M. den Nijs, Phys. Rev. B 37, 1766 (1988)

    Article  ADS  MathSciNet  Google Scholar 

  61. J.D. Kimel, P.A. Rikvold, Y.-L. Wang, Phys. Rev. B 45, 7237 (1992)

    Article  ADS  Google Scholar 

  62. S.L.A. de Queiroz, J. Phys. A: Math. Gen. 33, 721 (2000)

    Article  ADS  Google Scholar 

  63. R.E. Belardinelli, V.D. Pereyra, Phys. Rev. E 75, 046701 (2007)

    Article  ADS  Google Scholar 

  64. C. Zhou, J. Su, Phys. Rev. E 78, 046705 (2008)

    Article  ADS  Google Scholar 

  65. F. Liang, J. Stat. Phys. 122, 511 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  66. S. Schneider, M. Mueller, W. Janke, Comput. Phys. Commun. 216, 1 (2017)

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Photon Science, School of Physics and Chemistry, Gwangju Institute of Science and Technology, Gwangju, 61005, South Korea

    Moonjung Jung & Dong-Hee Kim

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  1. Moonjung Jung
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  2. Dong-Hee Kim
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Correspondence to Dong-Hee Kim.

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Jung, M., Kim, DH. First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited. Eur. Phys. J. B 90, 245 (2017). https://doi.org/10.1140/epjb/e2017-80471-2

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