Para depositar en Docta Complutense, identifícate con tu correo @ucm.es en el SSO institucional. Haz clic en el desplegable de INICIO DE SESIÓN situado en la parte superior derecha de la pantalla. Introduce tu correo electrónico y tu contraseña de la UCM y haz clic en el botón MI CUENTA UCM, no autenticación con contraseña.

Universal critical behavior of the two-dimensional Ising spin glass

dc.contributor.authorFernández Pérez, Luis Antonio
dc.contributor.authorMarinari, E.
dc.contributor.authorMartín Mayor, Víctor
dc.contributor.authorParisi, G.
dc.contributor.authorRuiz Lorenzo, J. J.
dc.date.accessioned2023-06-18T06:55:11Z
dc.date.available2023-06-18T06:55:11Z
dc.date.issued2016-07-01
dc.description©2016 American Physical Society. This work was partially supported by the Ministerio de Economía y Competitividad (MINECO, Spain) through Grants No. FIS2012-35719-C02 and No. FIS2013-42840-P, and by the Junta de Extremadura (Spain), with partial contribution by the European Union (FEDER) through Grant No. GRU10158.
dc.description.abstractWe use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Economía y Competitividad (MINECO)/FEDER
dc.description.sponsorshipJunta de Extremadura
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/38910
dc.identifier.doi10.1103/PhysRevB.94.024402
dc.identifier.issn1098-0121
dc.identifier.officialurlhttp://dx.doi.org/10.1103/PhysRevB.94.024402
dc.identifier.relatedurlhttp://journals.aps.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/24582
dc.issue.number2
dc.journal.titlePhysical review B
dc.language.isoeng
dc.page.final024402_10
dc.page.initial024402_1
dc.publisherAmerican Physical Society
dc.relation.projectIDFIS2012-35719-C02; FIS2013-42840-P
dc.relation.projectIDGRU10158
dc.rights.accessRightsopen access
dc.subject.cdu53
dc.subject.keywordMonte-Carlo simulations
dc.subject.keywordGround-state
dc.subject.keywordModel
dc.subject.keywordAlgorithm
dc.subject.keywordDimensions
dc.subject.ucmFísica (Física)
dc.subject.unesco22 Física
dc.titleUniversal critical behavior of the two-dimensional Ising spin glass
dc.typejournal article
dc.volume.number94
dcterms.references1. S. F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975). 2. K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986). 3. M. Mézard, G. Parisi, and M. Virasoro, Spin-Glass Theory and Beyond (World Scientific, Singapore, 1987). 4. K. Fisher and J. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991). 5. A. P. Young, Spin Glasses and Random Fields (World Scientific, Singapore, 1998). 6. M. Mézard and A. Montanari, Information, Physics, and Computation (Oxford University Press, Oxford, UK, 2009). 7. K. Binder and W. Kob, Glassy Materials and Disordered Solids. An Introduction to Their Statistical Mechanics (World Scientific, Singapore, 2011). 8. S. Kirkpatrick, Phys. Rev. B 16, 4630 (1977). 9. I. Morgenstern and K. Binder, Phys. Rev. B 22, 288 (1980). 10. J. A. Blackman, Phys. Rev. B 26, 4987 (1982). 11. W. L. McMillan, Phys. Rev. B 28, 5216 (1983). 12. H. F. Cheung and W. L. McMillan, J. Phys. C 16, 7027 (1983). 13. R. N. Bhatt and A. P. Young, in Heidelberg Colloquium on Glassy Dynamics, Lecture Notes in Physics No. 275, edited by J. L. van Hemmen and I. Morgenstern (Springer, Berlin, 1987). 14. R. R. P. Singh and S. Chakravarty, Phys. Rev. Lett. 57, 245 (1986). 15. J.-S. Wang and R. H. Swendsen, Phys. Rev. B 38, 4840 (1988). 16. H. Freund and P. Grassberger, J. Phys. A 21, L801 (1988). 17. H. Freund and P. Grassberger, J. Phys. A 22, 4045 (1989). 18. J. A. Blackman and J. Poulter, Phys. Rev. B 44, 4374 (1991). 19. B. A. Berg and T. Celik, Phys. Rev. Lett. 69, 2292 (1992). 20. L. Saul and M. Kardar, Phys. Rev. E 48, R3221 (1993). 21. L. Saul and M. Kardar, Nucl. Phys. B 432, 641 (1994). 22. H. Rieger, L. Santen, U. Blasum, M. Diehl, M. Jünger, and G. Rinaldi, J. Phys. A 29, 3939 (1996). 23. H. Rieger, L. Santen, U. Blasum, M. Diehl, and M. Jünger, J. Phys. A 30, 8795 (1997). 24. A. K. Hartmann and A. P. Young, Phys. Rev. B 64, 180404 (2001). 25. A. C. Carter, A. J. Bray, and M. A. Moore, Phys. Rev. Lett. 88, 077201 (2002). 26. C. Amoruso, E. Marinari, O. C. Martin, and A. Pagnani, Phys. Rev. Lett. 91, 087201 (2003). 27. J. Lukic, A. Galluccio, E. Marinari, O. C. Martin, and G. Rinaldi, Phys. Rev. Lett. 92, 117202 (2004). 28. T. Jörg, J. Lukic, E. Marinari, and O. C. Martin, Phys. Rev. Lett. 96, 237205 (2006). 29. J. Lukic, E. Marinari, O. C. Martin, and S. Sabatini, J. Stat. Mech. (2006) L10001. 30. F. Liers, J. Lukic, E. Marinari, A. Pelissetto, and E. Vicari, Phys. Rev. B 76, 174423 (2007). 31. H. G. Katzgraber, L. W. Lee, and I. A. Campbell, Phys. Rev. B 75, 014412 (2007). 32. F. Parisen Toldin, A. Pelissetto, and E. Vicari, Phys. Rev. E 82, 021106 (2010). 33. C. K. Thomas, D. A. Huse, and A. A. Middleton, Phys. Rev. Lett. 107, 047203 (2011). 34. F. Parisen Toldin, A. Pelissetto, and E. Vicari, Phys. Rev. E 84, 051116 (2011). 35. T. Jörg and F. Krzakala, J. Stat. Mech. (2012) L01001. 36. P. H. Lundow and I. A. Campbell, Phys. Rev. E 93, 022119 (2016). 37. S. Guchhait and R. Orbach, Phys. Rev. Lett. 112, 126401 (2014). 38. S. Guchhait, G. G. Kenning, R. L. Orbach, and G. F. Rodriguez, Phys. Rev. B 91, 014434 (2015). 39. S. Guchhait and R. L. Orbach, Phys. Rev. B 92, 214418 (2015). 40. N. G. Fytas and V. Martín-Mayor, Phys. Rev. Lett. 110, 227201 (2013). 41. F. Belletti, M. Cotallo, A. Cruz, L. A. Fernandez, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martín-Mayor, A. M. Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J. J. Ruiz-Lorenzo, S. F. Schifano, D. Sciretti, A. Tarancon, R. Tripiccione, J. L. Velasco, and D. Yllanes (Janus Collaboration), Phys. Rev. Lett. 101, 157201 (2008). 42. F. Belletti, A. Cruz, L. A. Fernandez, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martín-Mayor, J. Monforte, A. Muñoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J. J. Ruiz-Lorenzo, S. F. Schifano, D. Sciretti, A. Tarancon, R. Tripiccione, and D. Yllanes (Janus Collaboration), J. Stat. Phys. 135, 1121 (2009). 43. L. A. Fernández and V. Martín-Mayor, Phys. Rev. B 91, 174202 (2015). 44. M. Hasenbusch, A. Pelissetto, and E. Vicari, J. Stat. Mech. (2008) L02001. 45. When the critical temperature Tc is nonzero the problems caused by the nonlinear scaling fields can be bypassed using a standard analysis [50, 68, 69]. In fact in 3D spin glasses [70] one compares data from different system sizes at the same temperature, namely Tc, which cures most of the problems. 46. C. K. Thomas and A. A. Middleton, Phys. Rev. E 87, 043303 (2013). 47. F. Cooper, B. Freedman, and D. Preston, Nucl. Phys. B 210, 210 (1982). 48. M. Palassini and S. Caracciolo, Phys. Rev. Lett. 82, 5128 (1999). 49. H. G. Ballesteros, A. Cruz, L. A. Fernandez, V. Martín-Mayor, J. Pech, J. J. Ruiz-Lorenzo, A. Tarancon, P. Tellez, C. L. Ullod, and C. Ungil, Phys. Rev. B 62, 14237 (2000). 50. D. J. Amit and V. Martín-Mayor, Field Theory, the Renormalization Group and Critical Phenomena, 3rd ed. (World Scientific, Singapore, 2005). 51. J. Salas and A. D. Sokal, J. Stat. Phys. 98, 551 (2000). 52. The universality of the scaling functions in D=3 spatial dimensions was carefully analyzed in[71]. 53. G. Parisi, J. Stat. Phys. 23, 49 (1980). 54. S. Caracciolo, R. G. Edwards, S. J. Ferreira, A. Pelissetto, and A. D. Sokal, Phys. Rev. Lett.74, 2969 (1995). 55. S. Caracciolo, R. G. Edwards, A. Pelissetto, and A. D. Sokal, Phys. Rev. Lett. 75, 1891 (1995). 56. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Clarendon, Oxford, 1999). 57. The elementary Monte Carlo step consisted of ten Metropolis sweeps at fixed temperature, followed by a cluster update [60] and by a parallel tempering step [61, 62]. We consider two sets of two real replicas for each temperatures. The cluster updates are performed only within each set (overlaps are computed by taking a pair of statistically independent configurations, each from one set). We performed a stringent equilibration test that takes into account the statistical correlation when comparing the last logarithmic bins [72]. 58. Data for the Gaussian model can be fit as well with a subleading correction term L−2ω, rather than with the L−2 term we use in Eq. (9). With either subleading term we found that the leading corrections to the Gaussian data vanish within numerical accuracy. 59. The tentative estimate of Ref. [22] was later found to be problematic [23] . 60. J. Houdayer, Eur. Phys. J. B 22, 479 (2001). 61. K. Hukushima and K. Nemoto, J. Phys. Soc. Jpn. 65, 1604 (1996). 62. E. Marinari, in Advances in Computer Simulation, edited by J. Kerstész and I. Kondor (Springer, Berlin, 1998). 63. Another general solution is to use a discrete approximation to the Gaussian distribution, such as the Gaussian-Hermite quadrature [73]. For instance, in Refs. [74, 75] a Gaussian-distributed magnetic field was simulated in this way. 64. This situation is not desirable [76], but it is almost automatically enforced by the standard thermalization tests for spin glasses [72] . 65. R. Alvarez Baños, A. Cruz, L. A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martín-Mayor, J. Monforte-Garcia, A. Muñoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J. J. Ruiz-Lorenzo, S. F. Schifano, B. Seoane, A. Tarancon, R. Tripiccione, and D. Yllanes (Janus Collaboration), J. Stat. Mech. (2010) P06026. 66. 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, J. Stat. Mech. (2014) P05014. 67. For Lmin=32, the automated selection of T2max,ξL/L for the fits discussed in Appendix pp1-s2does not result into a good data collapse. For instance, for Gaussian couplings, ξL/L=0.1 and Lmin≥32 one needs to chose T2max,ξL/L=0.53 (rather than 0.8, as we choose for smaller Lmin). 68. M. Nightingale, Physica A 83, 561 (1976). 69. H. G. Ballesteros, L. A. Fernandez, V. Martín-Mayor, and A. Muñoz Sudupe, Phys. Lett. B 378, 207 (1996). 70. M. Baity-Jesi, R. A. Baños, A. Cruz, L. A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, D. Iniguez, A. Maiorano, F. Mantovani, E. Marinari, V. Martín-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 (Janus Collaboration),Phys. Rev. B 88, 224416 (2013). 71. T. Jörg, Phys. Rev. B 73, 224431 (2006). 72. L. A. Fernandez, A. Maiorano, E. Marinari, V. Martín-Mayor, D. Navarro, D. Sciretti, A. Tarancon, and J. L. Velasco, Phys. Rev. B 77, 104432 (2008). 73. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables., 9th ed. (Dover, New York, 1972). 74. L. Leuzzi, G. Parisi, F. Ricci-Tersenghi, and J. J. Ruiz-Lorenzo, Phys. Rev. Lett. 103, 267201 (2009). 75. M. Baity-Jesi, R. A. Baños, A. Cruz, L. A. Fernandez, J. M. Gil-Narvion, A. Gordillo-Guerrero, D. Iñiguez, A. Maiorano, M. 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. E 89, 032140 (2014). 76. H. G. Ballesteros, L. A. Fernandez, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, and J. J. Ruiz-Lorenzo, Nucl. Phys. B 512, 681 (1998).
dspace.entity.typePublication
relation.isAuthorOfPublication146096b1-5825-4230-8ad9-b2dad468673b
relation.isAuthorOfPublication061118c0-eadf-4ee3-8897-2c9b65a6df66
relation.isAuthorOfPublication.latestForDiscovery146096b1-5825-4230-8ad9-b2dad468673b

Download

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
MartínMayorV LIBRE 43.pdf
Size:
561.48 KB
Format:
Adobe Portable Document Format

Collections