Critical behavior of the three-dimensional Ising spin glass
Loading...
Official URL
Full text at PDC
Publication date
2000
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Citation
1) K. Binder, A. P. Young, Rev. Mod. Phys., 58, 801 (1986)
-- M. Mézard, G. Parisi, M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987)
-- K. H. Fisher, J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, U.K., 1991).
2) G. Parisi, Phys. Lett., 73A, 203 (1979)
-- ibid., J. Phys. A, 13, L115 (1980)
-- ibid., 13, 1101 (1980)
-- ibid., 13, 1887 (1980).
3) J. A. Mydosh, Spin Glasses: An Experimental Introduction (Taylor & Francis, London 1993).
4) See, for example, the following recent papers: M. Palassini and A. P. Young, Phys. Rev. Lett., 83, 5126 (1999)
-- cond-mat/0004485
-- E Marinari, G. Parisi, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, F. Zuliani, J. Stat. Phys., 98, 973 (2000)
-- E. Marinari, G. Parisi, cond-mat/0005047.
5) K. Gunnarsson, et al., Phys. Rev. B, 43, 8199 (1991).
-- See also P. Norblad and P. Svendlidh, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1997).
6) C. de Dominicis, I. Kondor, T. Temesvári, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1997).
7) N. Kawashima, A. P. Young, Phys. Rev. B, 53, R484 (1996).
8) D. Íñiguez, G. Parisi, J. J. Ruiz-Lorenzo, J. Phys. A, 29, 4337 (1996).
9) E. Marinari, G. Parisi, J. J. Ruiz-Lorenzo, Phys. Rev. B, 58, 14, 852 (1998).
10) D. Íñiguez, E. Marinari, G. Parisi, J. J. Ruiz-Lorenzo, J. Phys. A, 30, 7337 (1997).
11) B. A. Berg, W. Janke, Phys. Rev. Lett., 80, 4771 (1998)
-- W. Janke, B. A. Berg, A. Billoire, Ann. Phys (Leipzig) 7, 544 (1998).
12) M. Palassini, X. Caracciolo, Phys. Rev. Lett., 82, 5128 (1999).
13) A. T. Ogielski, Phys. Rev. B, 32, 7384 (1985).
14) R. N. Bahtt, A. P. Young, Phys. Rev. Lett., 54, 924 (1985).
15) R. N. Bahtt, A. P. Young, Phys. Rev. B, 37, 5606 (1988).
16) M. Tesi, E. Janse van Resburg, E. Orlandini, S. G. Whillington, J. Stat. Phys., 82, 155 (1996)
-- K. Hukushima, K. Nemoto, J. Phys. Soc. Jpn., 65, 1604 (1996).
17) E. Marinari, Optimized Monte Carlo Methods, Lecture Notes in Physics Vol. 501 (Springer-Verlag, Heidelberg, 1998).
18) E. Marinari, G. Parisi, J. J. Ruiz-Lorenzo, in Numerical Simulations of Spin Glass Systems in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore, 1997).
19) F. Cooper, B. Freedman, D. Preston, Nucl. Phys. B, 210, 210 (1989).
20) See, for instance, M. N. Barber, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London, 1983), Vol. 8.
21) M. Lüsher, P. Weisz, U. Wolff, Nucl. Phys. B, 359, 221 (1991)
-- J.-K. Kim, Phys. Rev. Lett., 70, 1735 (1993)
-- S. Caracciolo, R. G. Edwards, S. J. Ferreira, A. Sokal, ibid., 74, 2969 (1995)
-- S. Caracciolo, R. G. Edwards, A. Sokal, ibid., 75, 1891 (1995).
22) H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, Phys. Lett. B, 378, 207 (1996)
-- ibid., Nucl. Phys. B, 483, 707 (1997).
23) J. Kisker, L. Santen, M. Schreckenberg, H. Rieger, Phys. Rev. B, 53, 6418 (1996)
-- E. Marinari, G. Parisi, J. J. Ruiz-Lorenzo, F. Ritort, Phys. Rev. Lett., 76, 843 (1996)
-- Y. G. Joh, R. Orbach, G. G. Wood, J. Hammann, E. Vincent, ibid., 82, 438 (1999)
-- G. Parisi, E. Marinari, F. Ricci-Tersenghi, J. J. Ruiz-Lorenzo, J. Phys. A, 33, 2373 (2000).
24) H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, J. J. Ruiz-Lorenzo, Phys. Lett. B, 400, 346 (1997)
-- ibid., Nucl. Phys. B, 512[FS], 681 (1998)
-- ibid., Phys. Rev. B, 58, 2740 (1998).
25) E. Marinari, V. Martín-Mayor, A. Pagnani, Phys. Rev. B, 62, 4999 (2000).
26) F. Ritort, M. Sales, J. Phys. A, 33, 6505 (2000).
27) K. Binder, Z. Phys. B: Condens. Matter, 43, 119 (1981).
28) E. Marinari, C. Naitza, G. Parisi, M. Picco, F. Ritort, F. Zuliani, Phys. Rev. Lett., 81, 1698 (1998).
29) J. Pech, A. Tarancón, C. L. Ullod, Comput. Phys. Commun., 106, 10 (1997).
30) J. J. Ruiz-Lorenzo, C. L. Ullod, Comput. Phys. Commun., 125, 210 (2000).
31) A. Cruz, J. Pech, A. Tarancón, P. Téllez, C. L. Ullod, C. Ungil, cond-mat/0004080 (unpublished).
32) H. G. Ballesteros, V. Martín-Mayor, Phys. Rev. E, 58, 6787 (1998).
33) M. Falcioni, E. Marinari, M. L. Paciello, G. Parisi, B. Taglienti, Phys. Lett., 108B, 331 (1982)
-- A. M. Ferrenberg, R. H. Swendsen, Phys. Rev. Lett., 61, 2635 (1988).
34) A. D. Sokal, in Quantum Fields on the Computer, Advanced Series on Directions in High Energy Physics, Vol. 11, edited by M. Creutz (World Scientific, Singapore, 1992).
35) We have simulated the two-dimensional XY model using the Wolff single-cluster algorithm (Ref. 36). We have done different runs, near the critical point b.1.11, on lattice sizes L516, 32, and 64, using the spectral density method in the analysis of the data.
36) U. Wolff, Phys. Rev. Lett., 62, 361 (1989).
37) J. Salas, A. D. Sokal, cond-mat/9904038 (unpublished).
Abstract
We have simulated, using parallel tempering, the three-dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (L520) has been studied using a dedicated computer (the SUE machine). We have obtained, measuring the correlation length in the critical region, strong evidence for a second-order finite-temperature phase transition, ruling out other possible scenarios like a KosterlitzThouless phase transition. Precise values for the ν and ƞ critical exponents are also presented.
Description
© 2000 The American Physical Society. We acknowledge discussions with E. Marinari and G. Parisi. We are grateful for the partial financial support from CICyT (AEN97-1680, AEN97-1693, AEN99-0990, and PB98-0842) and DGA (P46/97). V.M-M. was supported by a M.E.C. The computations have been carried out using the RTNN machines (Universidad de Zaragoza and Universidad
Complutense de Madrid) and the dedicated machine SUE
(Universidad de Zaragoza).