Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

Physical Review B - Condensed Matter and Materials Physics

Volumn 80, Issue 2, 2009, Pages

  Fernandez, L A ^a,b   Martin Mayor, V ^a,b   Perez Gaviro, S ^b,c   Tarancon, A ^b   Young, A P ^d  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITY OF ZARAGOZA   (Spain)

^c UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 69549131001     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.80.024422     Document Type: Article

References (26)

1. H. G. Ballesteros, A. Cruz, L. A. Fernandez, V. Martin-Mayor, J. Pech, J. J. Ruiz-Lorenzo, A. Tarancon, P. Tellez, C. L. Ullod, and C. Ungil, Phys. Rev. B 62, 14237 (2000). 10.1103/PhysRevB.62.14237
2. H. G. Katzgraber, M. Körner, and A. P. Young, Phys. Rev. B 73, 224432 (2006). 10.1103/PhysRevB.73.224432
3. M. Hasenbusch, A. Pelissetto, and E. Vicari, Phys. Rev. B 78, 214205 (2008). 10.1103/PhysRevB.78.214205
4. R. Omari, J. J. Prejean, and J. Souletie, J. Phys. (Paris) 44, 1069 (1983).
5. H. Kawamura, Phys. Rev. Lett. 80, 5421 (1998). 10.1103/PhysRevLett.80. 5421
6. K. Hukushima and H. Kawamura, Phys. Rev. B 72, 144416 (2005). 10.1103/PhysRevB.72.144416
7. L. W. Lee and A. P. Young, Phys. Rev. Lett. 90, 227203 (2003). 10.1103/PhysRevLett.90.227203
8. I. Campos, M. Cotallo-Aban, V. Martin-Mayor, S. Perez-Gaviro, and A. Tarancon, Phys. Rev. Lett. 97, 217204 (2006). 10.1103/PhysRevLett.97.217204
9. L. W. Lee and A. P. Young, Phys. Rev. B 76, 024405 (2007). 10.1103/PhysRevB.76.024405
10. D. X. Viet and H. Kawamura, Phys. Rev. Lett. 102, 027202 (2009). 10.1103/PhysRevLett.102.027202
11. D. X. Viet and H. Kawamura, arXiv:0904.3699 (unpublished).
12. To our knowledge, a 483 lattice is the largest spin glass that has been thermalized near a finite-temperature phase transition. It is curious that larger sizes can be studied for the Heisenberg model than for the Ising cases [for which the 283 samples studied by Hasenbusch (Ref.) seems to be the record], even though the updating code is more complicated. Evidently, the barriers between valleys are lower in the Heisenberg model.
13. B. Cooper, B. Freedman, and D. Preston, Nucl. Phys. B 210, 210 (1982). 10.1016/0550-3213(82)90240-1
14. M. Palassini and S. Caracciolo, Phys. Rev. Lett. 82, 5128 (1999). 10.1103/PhysRevLett.82.5128
15. D. Amit and V. Matin-Mayor, Field Theory, the Renormalization Group and Critical Phenomena (World Scientific, Singapore, 2005).
16. For the CG, one considers a transverse or parallel ξCG,L, depending on whether μI kmin =0 or not (Refs.). We report only the parallel ξCG,L as the two coincide within errors.
17. K. Binder, Z. Phys. B: Condens. Matter 43, 119 (1981). 10.1007/BF01293604
18. H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, and A. Muñoz Sudupe, Phys. Lett. B 387, 125 (1996). 10.1016/0370-2693(96)00984-7
19. M. P. Nightingale, Physica A 83, 561 (1975). 10.1016/0378-4371(75)90021-7
20. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996). 10.1143/JPSJ.65.1604
21. J. H. Pixley and A. P. Young, Phys. Rev. B 78, 014419 (2008). 10.1103/PhysRevB.78.014419
22. H. G. Katzgraber, M. Palassini, and A. P. Young, Phys. Rev. B 63, 184422 (2001). 10.1103/PhysRevB.63.184422
23. Given the set of temperatures {Ti}, let f (T) be a cubic polynomial in T-1 (unique up to an irrelevant multiplicative constant) with i f (Ti) =0 and f′ (Tmax) =0, and changing sign at 0.14 Tc. Let ft be f (T) for the T occupied by one copy of the system at time t. We first coarse grain ft by averaging over 100 consecutive MC sweeps and then compute its autocorrelation function and integrated autocorrelation time (Refs.).
24. L. A. Fernandez and V. Martin-Mayor, Phys. Rev. E 79, 051109 (2009). 10.1103/PhysRevE.79.051109
25. The T SG,CG (L,sL) are statistically correlated, so one should use the full covariance matrix to compute χ2. However, we find that considering only diagonal covariances does not significantly change the results. We give results obtained with diagonal covariances since these can be reproduced from the data in Table 2.
26. A. Sokal, in Functional Integration: Basics and Applications, edited by, C. DeWitt-Morette, P. Cartier and, A. Folacci, (Plenum, New York, 1997)