Publication: Critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions
Loading...
Official URL
Full text at PDC
Publication Date
2008-03-24
Authors
Maiorano, A.
Marinari, E.
Navarro, D.
Sciretti, D.
Tarancón, A.
Velasco, J. L.
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Citations
Exportar
Abstract
We investigate the critical properties of the four-state commutative random permutation glassy Potts model in three and four dimensions by means of Monte Carlo simulations and a finite-size scaling analysis. By using a field programmable gate array, we have been able to thermalize a large number of samples of systems with large volume. This has allowed us to observe a spin-glass ordered phase in d=4 and to study the critical properties of the transition. In d=3, our results are consistent with the presence of a Kosterlitz-Thouless transition, but also with different scenarios: transient effects due to a value of the lower critical dimension slightly below 3 could be very important.
Description
© 2008 The American Physical Society. We acknowledge partial financial support from CAM-UCM and UCM-BSCH, and from MEC through research contracts Nos. FIS2006-08533-C03 and TEC2007-64188. J.L.V. is supported by DGA. We thank Stefano Mossa, Giorgio Parisi, and Cristina Picus for a number of conversations about the glassy Potts models and more. We thank Raffaele Tripiccione and all the JANUS Collaboration for their continuous help, which could not have been more important for us.
UCM subjects
Unesco subjects
Keywords
Citation
1) E. Gardner, Nucl. Phys. B, 257, 747, 1985.
2) D. Elderfield, D. Sherrington, J. Phys. C, 16, L497, 1983.
3) D. Elderfield, D. Sherrington, J. Phys. C, 16, L971, 1983.
4) D. J. Gross, I. Kanter, H. Sompolinsky, Phys. Rev. Lett., 55, 304, 1985.
5) H. Nishimori, M. J. Stephen, Phys. Rev. B, 27, 5644, 1983.
6) E. Marinari, S. Mossa, G. Parisi, Phys. Rev. B, 59, 8401, 1999.
7) S. Franz, M. Mézard, F. Ricci-Tersenghi, M. Weigt, R. Zecchina, Europhys. Lett., 55, 465, 2001.
8) A. Cavagna, I. Giardina, T. S. Grigera, Europhys. Lett., 61, 74, 2003
-- A. Cavagna, I. Giardina, T. S. Grigera, J. Chem. Phys., 118, 6974, 2003.
9) F. Krzakala, L. Zdeborová, EPL, 81, 57005, 2008.
10) K. Binder, J. D. Reger, Adv. Phys., 41, 547, 1992.
11) See, e.g., M. Mézard, G. Parisi, M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore) 1987.
12) D. J. Gross, M. Mézard, Nucl. Phys. B, 240, 431, 1984.
13) T. R. Kirkpatrick, P. G. Wolynes, Phys. Rev. B, 36, 8552, 1987.
14) T. R. Kirkpatrick, D. Thirumalai, Phys. Rev. B, 37, 5342, 1988.
15) W. Götze, L. Sjögren, Rep. Prog. Phys., 55, 241, 1992.
16) J. P. Bouchaud, L. F. Cugliandolo, J. Kurchan, M. Mézard, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore) 1997.
17) K. Binder, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore) 1997.
18) J. R. Banavar, M. Cieplak, Phys. Rev. B, 39, 9633, 1989.
19) J. R. Banavar, M. Cieplak, Phys. Rev. B, 40, 4613, 1989.
20) M. Scheucher, J. D. Reger, K. Binder, A. P. Young, Phys. Rev. B, 42, 6881, 1990.
21) M. Scheucher, J. D. Reger, Phys. Rev. B, 45, 2499, 1992.
22) M. Reuhl, P. Nielaba, K. Binder, Eur. Phys. J. B, 2, 225, 1998.
23) O. Carmesin, K. Binder, J. Phys. A, 21, 4053, 1988.
24) R. R. P. Singh, Phys. Rev. B, 43, 6299, 1991.
25) B. Lobe, W. Janke, K. Binder, Eur. Phys. J. B, 7, 283, 1999.
26) L. W. Lee, H. G. Katzgraber, A. P. Young, Phys. Rev. B, 74, 104416, 2006.
27) C. Brangian, W. Kob, K. Binder, Europhys. Lett., 59, 546, 2002.
28) C. Brangian, W. Kob, K. Binder, J. Phys. A, 36, 10847, 2003.
29) M. P. Eastwood, P. G. Wolynes, Europhys. Lett., 60, 587, 2002.
30) G. Toulouse, Commun. Phys. (London), 2, 115, 1977.
31) D. M. Carlucci, Phys. Rev. B, 60, 9862, 1999.
32) F. Belletti, M. Cotallo, A. Cruz, L. A. Fernández, A. Gordillo, A. Maiorano, F. Mantovani, E. Marinari, V. Martín-Mayor, A. Muñoz-Sudupe, D. Navarro, S. Pérez- Gaviro, J. J. Ruiz Lorenzo, S. F. Schifano, D. Sciretti, A. Tarancón, R. Tripiccione, J. L. Velasco, Comput. Phys. Commun., 178, 208, 2008.
33) E. Marinari, G. Parisi, J. J. Ruiz-Lorenzo, in Spin Glasses and Random Fields, edited by A. P. Young (World Scientific, Singapore) 1997.
34) B. Cooper, B. Freedman, D. Preston, Nucl. Phys. B, 210, 210, 1982.
35) D. Amit, V. Martín-Mayor, Field Theory, the Renormalization Group and Critical Phenomena, 3rd ed. (World-Scientific, Singapore) 2005.
36) M. Falcioni, E. Marinari, M. L. Paciello, G. Parisi, B. Taglienti, Phys. Lett., 108B, 331, 1982.
37) A. M. Ferrenberg, R. H. Swendsen, Phys. Rev. Lett., 61, 2635, 1988.
38) H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, J. J. Ruiz-Lorenzo, Nucl. Phys. B, 512, 681, 1998.
39) H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, Phys. Lett. B, 378, 207, 1996.
40) H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, Nucl. Phys. B, 483, 707, 1997.
41) G. Parisi, F. Rapuano, Phys. Lett., 157B, 301, 1985. 42) J. M. Kosterlitz, D. J. Thouless, J. Phys. C, 6, 1181, 1973.
43) A. Cruz, J. Pech, A. Tarancón, P. Téllez, C. L. Ullod, C. Ungil, Comput. Phys. Commun., 133, 165, 2001.