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Phase transition in three-dimensional Heisenberg spin glasses with strong random anisotropies through a multi-GPU parallelization

M. Baity-Jesi1,2,3,*, L. A. Fernández1,2, V. Martín-Mayor1,2, and J. M. Sanz1

  • 1Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain
  • 2Instituto de Biocomputación and Física de Sistemas Complejos (BIFI), 50009 Zaragoza, Spain
  • 3Dipartimento di Fisica, Università La Sapienza, 00185 Roma, Italy

  • *marcobaityjesi@fis.ucm.es
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Phys. Rev. B 89, 014202 – Published 21 January, 2014

DOI: https://doi.org/10.1103/PhysRevB.89.014202

Abstract

We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark on the presence of strong finite-size effects in the chiral sector. On the spin glass sector, we find that the universality class is that of Ising spin glasses. Our data are compatible with a unique phase transition for the chiral and spin glass sector. We focus on keeping finite-size effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to 643 spins, over a vast range of temperatures (hence, of relaxation times).

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References (89)

  1. M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
  2. J. A. Mydosh, Spin Glasses: An Experimental Introduction (Taylor and Francis, London 1993).
  3. A. P. Young, Spin Glasses and Random Fields (World Scientific, Singapore, 1997).
  4. M. A. Ruderman and C. Kittel, Phys. Rev. 96, 99 (1954).
  5. T. Kasuya, Prog. Theor. Phys. 16, 45 (1956).
  6. K. Yosida, Phys. Rev. 106, 893 (1957).
  7. I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958).
  8. T. Moriya, Phys. Rev. Lett. 4, 228 (1960).
  9. S. F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975).
  10. D. Petit, L. Fruchter, and I. A. Campbell, Phys. Rev. Lett. 88, 207206 (2002).
  11. F. Bert, V. Dupuis, E. Vincent, J. Hammann, and J.-P. Bouchaud, Phys. Rev. Lett. 92, 167203 (2004).
  12. O. E. Peil, A. V. Ruban, and B. Johansson, Phys. Rev. B 79, 024428 (2009).
  13. J. W. Cable, S. A. Werner, G. P. Felcher, and N. Wakabayashi, Phys. Rev. Lett. 49, 829 (1982).
  14. J. W. Cable, S. A. Werner, G. P. Felcher, and N. Wakabayashi, Phys. Rev. B 29, 1268 (1984).
  15. F. J. Lamelas, S. A. Werner, S. M. Shapiro, and J. A. Mydosh, Phys. Rev. B 51, 621 (1995).
  16. H. Bouchiat, J. Phys. (Paris) 47, 71 (1986).
  17. L. P. Lévy, Phys. Rev. B 38, 4963 (1988).
  18. K. Gunnarsson, P. Svedlindh, P. Nordblad, L. Lundgren, H. Aruga, and A. Ito, Phys. Rev. B 43, 8199 (1991).
  19. S. Franz, G. Parisi, and M. A. Virasoro, J. Phys. I France 4, 1657 (1994).
  20. M. Palassini and S. Caracciolo, Phys. Rev. Lett. 82, 5128 (1999).
  21. H. G. Ballesteros, A. Cruz, L. A. Fernández, V. Martín-Mayor, J. Pech, J. J. Ruiz-Lorenzo, A. Tarancón, P. Téllez, C. L. Ullod, and C. Ungil, Phys. Rev. B 62, 14237 (2000).
  22. W. L. McMillan, Phys. Rev. B 31, 342 (1985).
  23. J. A. Olive, A. P. Young, and D. Sherrington, Phys. Rev B 34, 6341 (1986).
  24. B. M. Morris et al., J. Phys. C 19, 1157 (1986).
  25. F. Matsubara, T. Iyota, and S. Inawashiro, Phys. Rev. Lett. 67, 1458 (1991).
  26. M. J. P. Gingras, Phys. Rev. Lett. 71, 1637 (1993).
  27. B. Coluzzi, J. of Phys. A: Math. Gen. 28, 747 (1995).
  28. A. Mauger, J. Villain, Y. Zhou, C. Rigaux, N. Bontemps, and J. Férré, Phys. Rev. B 41, 4587 (1990).
  29. H. Kawamura, Phys. Rev. Lett. 68, 3785 (1992); 80, 5421 (1998).
  30. L. W. Lee and A. P. Young, Phys. Rev. Lett. 90, 227203 (2003).
  31. L. A. Fernandez, V. Martin-Mayor, S. Perez-Gaviro, A. Tarancon, and A. P. Young, Phys. Rev. B 80, 024422 (2009).
  32. I. Campos, M. Cotallo-Aban, V. Martin-Mayor, S. Perez-Gaviro, and A. Tarancon, Phys. Rev. Lett. 97, 217204 (2006).
  33. D. X. Viet and H. Kawamura, Phys. Rev. Lett. 102, 027202 (2009).
  34. H. Kawamura, Phys. Rev. Lett. 90, 047202 (2003).
  35. T. Taniguchi, J. Phys.: Condens. Matter 19, 145213 (2007).
  36. I. A. Campbell and D. C. M. C. Petit, J. Phys. Soc. Jpn. 79, 011006 (2010).
  37. D. Amit and V. Martin-Mayor, Field Theory, the Renormalization Group and Critical Phenomena, 3rd ed. (World Scientific, Singapore, 2005).
  38. F. Belletti et al., Phys. Rev. Lett. 101, 157201 (2008); , J. Stat. Phys. 135, 1121 (2009).
  39. Y. G. Joh, R. Orbach, G. G. Wood, J. Hammann, and E. Vincent, Phys. Rev. Lett. 82, 438 (1999).
  40. A. J. Bray and M. A. Moore, J. Phys. C: Solid State Phys. 15, 3897 (1982).
  41. V. Martin-Mayor and S. Perez-Gaviro, Phys. Rev. B 84, 024419 (2011).
  42. Recall that γCG=ν(2−ηCG), where γCG is the critical index for the CG susceptibility, while ν is the correlation-length exponent.
  43. Of course the limiting factor is in the wide range of relaxation times, rather than temperatures. However, relaxation times depend on a variety of implementation-dependent factors (such as the temperature spacing in the parallel tempering, or the number of over-relaxation sweeps). Hence, comparison with other work will be easier in terms of temperatures.
  44. National Super-Computing Center, Tianjin, China, http://www.nscc-tj.gov.cn/en/
  45. Barcelona Supercomputing Center, Barcelona, Spain, http://www.bsc.es
  46. F. Parisen Toldin, A. Pelissetto, and E. Vicari, J. Stat. Mech. (2006) P06002.
  47. F. Liers, J. Lukic, E. Marinari, A. Pelissetto, and E. Vicari, Phys. Rev. B 76, 174423 (2007).
  48. Independence from microscopic details such as the disorder distribution has been found for spin glasses [[49, 50, 51, 52]], as well as for other disordered systems like the random field Ising model [53], or disordered ferromagnets (either site [54] or bond [[55], [56]] diluted).
  49. M. Hasenbusch, A. Pelissetto, and E. Vicari, Phys. Rev. B 78, 214205 (2008).
  50. T. Jorg, Phys. Rev. B 73, 224431 (2006).
  51. H. G. Katzgraber, M. Korner, and A. P. Young, Phys. Rev. B 73, 224432 (2006).
  52. T. Jorg and H. G. Katzgraber, Phys. Rev. Lett. 101, 197205 (2008).
  53. N. G. Fytas and V. Martin-Mayor, Phys. Rev. Lett. 110, 227201 (2013).
  54. H. G. Ballesteros, L. A. Fernandez, V. Martin-Mayor, A. Munoz Sudupe, G. Parisi and J. J. Ruiz-Lorenzo, Phys. Rev. B 58, 2740 (1998).
  55. P.-E. Berche, C. Chatelain, B. Berche, and W. Janke, Eur. Phys. J. B 38, 463 (2004).
  56. A. Malakis, A. N. Berker, N. G. Fytas, and T. Papakonstantinou, Phys. Rev. E 85, 061106 (2012).
  57. M. Baity-Jesi et al., Eur. Phys. J. Special Topics 210, 33 (2012).
  58. L. W. Lee and A. P. Young, Phys. Rev. B 76, 024405 (2007).
  59. F. R. Brown and T. J. Woch, Phys. Rev. Lett. 58, 2394 (1987).
  60. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn 65, 1604 (1996).
  61. E. Marinari in Advances in Computer Simulations, edited by J. Kerstész and I. Kondor (Springer, Berlin, 1995).
  62. J. L. Alonso, A. Tarancón, H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, and A. Muñoz Sudupe, Phys. Rev. B 53, 2537 (1996).
  63. E. Marinari, V. Martin-Mayor, and A. Pagnani, Phys. Rev. B 62, 4999 (2000).
  64. It is enough to define the local field as hx⃗=∑∥x−y∥=1[Jxys⃗y+Dxys⃗y].
  65. L. A. Fernández, A. Maiorano, E. Marinari, V. Martin-Mayor, D. Navarro, D. Sciretti, A. Tarancón, and J. L. Velasco, Phys. Rev. B 77, 104432 (2008).
  66. M. P. Nightingale, Physica A 83, 561 (1975).
  67. H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, and A. Muñoz-Sudupe, Phys. Lett. B 378, 207 (1996).
  68. A more recent article from the Janus Collaboration (Ref. [69]) gives a more precise determination of the critical exponents. Using one or the other does not change significantly our results and conclusions.
  69. Janus Collaboration: M. Baity-Jesi, R. A. Baños, A. Cruz, L. A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, D. Iñiguez, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, J. Monforte-Garcia, A. Muñoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, M. Pivanti, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, S. F. Schifano, B. Seoane, A. Tarancon, R. Tripiccione, and D. Yllanes, Phys. Rev. B 88, 224416 (2013).
  70. Some of the points we used for those extrapolations shared some of the data. For example, the crossing of ξ for L=8,16, had in common the points from size L=16 with the pair L=16,32. Hence, in the fits we have taken into account the covariance matrix that gave a measure of the anticorrelation between measures that share data.
  71. In Ref. [41] the Dijαβ are uniformly distributed between ±D=0.05, while in our work we use binary couplings. If we want to compare them, we have to use D=1/1200≃0.03.
  72. In the phase diagram we show the D=0 point comes from Ref. [31], where chiral and spin glass transition are assumed to be coupled. There is disagreement on whether TSG=TCG also in the isotropic case. Yet, we do plot it as a single transition because although TSG might be lower than TCG, their best estimates are compatible (and not distinguishable in the plot).
  73. In a typical system N=L3∼6×1023⇒L≃108.
  74. G. F. Rodriguez, G. G. Kenning, and R. Orbach, Phys. Rev. B 88, 054302 (2013).
  75. J. H. Pixley and A. P. Young, Phys. Rev. B 78, 014419 (2008).
  76. NVIDIA Corporation, CUDA C Programming Guide, docs.nvidia.com/cuda/cuda-c-programming-guide/index.html
  77. M. Baity-Jesi, Ph.D. thesis, Universidad Complutense de Madrid (work in progress).
  78. M. Bernaschi, G. Parisi, and L. Parisi, Comput. Phys. Commun. 182, 1265 (2011).
  79. T. Yavors'kii and M. Weigel, Eur. Phys. J. Special Topics 210, 159 (2012).
  80. D. E. Knuth, The Art of Computer Programming, 2nd ed. (Addison-Wesley, Reading, MA, 1981), Vol. 2.
  81. L. A. Fernandez, V. Martin-Mayor, and D. Yllanes, Nucl. Phys. B 807, 424 (2009).
  82. V. Parisi, cited in G. Parisi and F. Rapuano, Phys. Lett. B 157, 301 (1985).
  83. H. G. Ballesteros and V. Martin-Mayor, Phys. Rev. E 58, 6787 (1998).
  84. L. A. Fernandez, V. Martin-Mayor, D. Sciretti, A. Tarancon, and J. L. Velasco, Phys. Lett. B 628, 281 (2005).
  85. P. L'Ecuyer, Math. Comp. 68, 249 (1999).
  86. G. Ossola and A. D. Sokal, Nucl. Phys. B 691, 259 (2004).
  87. M. Luescher, Comput. Phys. Commun. 79, 100 (1994).
  88. G. Marsaglia, Diehard Battery of Tests of Randomness, http://www.stat.fsu.edu/pub/diehard
  89. R. J. Rivers, Path Integral Methods in Quantum Field Theories (Cambridge University Press, Cambridge, 1990).

Outline

Information

Phys. Rev. B 89, 014202– Published 21 January, 2014
  • Received 6 September 2013
  • Revised 18 December 2013

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