Publication:
The three-dimensional Ising spin glass in an external magnetic field: the role of the silent majority

Thumbnail Image
Files
FernándezPérezLuisAntonio71LIBRE PREPRINT.pdf (1.05 MB)
Official URL
http://doi.org/10.1088/1742-5468/2014/05/P05014
Full text at PDC
Publication Date
2014-05-16
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
IOP Publishing
Citations
Google Scholar
Exportar
DC QDC MarcXML RDF MODS METS ORE-ATOM
Research Projects
Organizational Units
Journal Issue
Abstract
We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field, using the Janus computer. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the model: Averages over all the data only describe the behaviour of a small fraction of it. Therefore we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where a part of the measurements behaves as the average, while the majority of them shows signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would be critical regime is unreachable with present resources, the numerical challenge is finally well posed.
Description
© 2014 IOP Publishing Ltd and SISSA Medialab srl. Artículo firmado por 24 autores. The Janus project has been partially supported by the EU (FEDER funds, No. UNZA05-33-003, MEC DGA, Spain), by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007–2013, ERC grant agreement No. 247328), by MINECO (Spain) (contracts FIS2012-35719-C02, FIS2010-16587, TEC2010-19207), by the SUMA project of INFN (Italy), by the Junta de Extremadura (GR10158) and by the European Union (PIRSES-GA 2011-295302). FR-T was supported by the Italian Research Ministry through the FIRB project No. RBFR086NN1, MB-J was supported by the FPU programme (Ministerio de Educación, Spain), RAB and JM-G were supported by the FPI programme (Diputación de Aragón, Spain) and SP-G was supported by the ARAID foundation; finally JMG-N was supported by the FPI programme (Ministerio de Economía, Spain).
UCM subjects
Física (Física) , Física-Modelos matemáticos
Unesco subjects
22 Física
Keywords
Citation
[1] Mydosh, J.A., 1993, Spin Glasses: an Experimental Introduction (London: Taylor and Francis). [2] Edwards, S.F., Anderson, P.W., 1975, J. Phys. F, 5, 965. [3] Edwards, S.F., Anderson, P.W., 1976, J. Phys. F, 6, 1927. [4] Mézard, M., Parisi, G., Virasoro, M., 1987, Spin-Glass Theory and Beyond (Singapore: World Scientific). [5] de Almeida, J.R.L., Thouless, D.J., 1978, J. Phys. A, 11, 983. [6] Marinari, E., Parisi, G., Ricci-Tersenghi, F., Ruiz-Lorenzo, J.J., Zuliani, F., 2000, J. Stat. Phys., 98, 973, (Preprint arXiv:cond-mat/9906076). [7] Parisi, G., 1979, Phys. Rev. Lett., 43, 1754. [8] Parisi, G., 1980, J. Phys. A: Math. Gen., 13, 1101. [9] Parisi, G., 1983, Phys. Rev. Lett., 50, 1946. [10] Parisi, G., Temesvári, T., 2012, Nucl. Phys. B, 858, 293 (Preprint arXiv:1111.3313). [11] McMillan, W.L., 1984, J. Phys. C: Solid State Phys., 17, 3179. [12] Bray, A.J., Moore, M.A., 1987, Scaling theory of the ordered phase of spin glasses Heidelberg Colloquium on Glassy Dynamics (Lecture Notes in Physics no 275) ed. van Hemmen, J.L. and Morgenstern, I. (Berlin: Springer). [13] Fisher, D.S., Huse, D.A., 1986, Phys. Rev. Lett., 56, 1601. [14] Fisher, D.S., Huse, D.A., 1988, Phys. Rev. B, 38, 386. [15] Moore, M.A., Bray, A.J., 2011, Phys. Rev. B, 83, 224408 (Preprint arXiv:1102.1675). [16] Yeo, J., Moore, M.A., 2012, Phys. Rev. E, 86, 052501 (Preprint arXiv:1208.3044). [17] Jönsson, P.E., Takayama, H., Katori, H.A., Ito, A., 2005, Phys. Rev. B, 71, 180412(R) (Preprint arXiv:cond-mat/0411291). [18] Petit, D., Fruchter, L., Campbell, I.A., 1999, Phys. Rev. Lett, 83, 5130 (Preprint arXiv:cond-mat/9910353). [19] Petit, D., Fruchter, L., Campbell, I.A., 2002, Phys. Rev. Lett, 88, 207206 (Preprint arXiv:cond-mat/011112). [20] Tabata, Y., Matsuda, K., Kanada, S., Yamazaki, T., Waki, T., Nakamura, H., Sato, K., Kindo, K., 2010, Journal of Physical Society of Japan, 79, 123704 (Preprint arXiv:1009.6115). [21] Bray, A.J., Moore, M.A., 1980, J. Phys. C: Solid St. Phys. C, 13, 419. [22] Temesvári, T., De Dominicis, C., 2002, Phys. Rev. Lett., 89, 097204 (Preprint arXiv:cond-mat/0207512). [23] Temesvári, T., 2008, Phys. Rev. B, 78, 220401. [24] Palassini, M., Caracciolo, S., 1999, Phys. Rev. Lett., 82, 5128–5131 (Preprint arXiv:cond-mat/9904246). [25] Ballesteros, H.G., Cruz, A., Fernández, L.A., Martín-Mayor, V., Pech, J., Ruiz-Lorenzo, J.J., Tarancón, A., Téllez, P., Ullod, C.L., Ungil C, 2000, Phys. Rev. B, 62, 14237–14245 (Preprint arXiv:cond-mat/0006211). [26] Gunnarsson, K., Svedlindh, P., Nordblad, P., Lundgren, L., Aruga, H., Ito, A., 1991, Phys. Rev. B, 43, 8199–8203. [27] Young, A.P., Katzgraber, H.G., 2004, Phys. Rev. Lett., 93, 207203 (Preprint arXiv:cond-mat/0407031). [28] Jörg, T., Katzgraber, H.G., Krzakala, F., 2008, Phys. Rev. Lett., 100, 197202 (Preprint arXiv:0712.2009). [29] Baños, R.A., Cruz, A., Fernández, L.A., Gil-Narvión, J.M., Gordillo-Guerrero, A., Guidetti, M., Iniguez, D., Maiorano, A., Marinari, E., Martín-Mayor, V., Monforte-García, J., Muñoz Sudupe, A., Navarro, D., Parisi, G., Pérez-Gaviro, S., Ruiz-Lorenzo, J.J., Schifano, S.F., Seoane, B., Tarancón, A., Téllez, P., Tripiccione, R., Yllanes, D., 2012, Proc. Natl. Acad. Sci. USA, 109, 6452. [30] Kotliar, G., Anderson, P.W., Stein, D.L., 1983, Phys. Rev. B, 27, 602. [31] Leuzzi, L., Parisi, G., Ricci-Tersenghi, F., Ruiz-Lorenzo, J.J., 2008, Phys. Rev. Lett., 101, 107203. [32] Larson, D., Katzgraber, H.G., Moore, M.A., Young, A.P., 2013, Phys. Rev. B, 87, 024414 (Preprint arXiv:1211.7297). [33] Leuzzi, L., Parisi, G., 2013, Phys. Rev. B, 88, 224204 (Preprint arXiv:1303.6333). [34] Baity-Jesi, M., Baños, R.A., Cruz, A., Fernández, L.A., Gil-Narvión, J.M., Gordillo-Guerrero, A., Iniguez, D., Maiorano, A., F. M., Marinari, E., Martín-Mayor, V., Monforte-García, J., Muñoz Sudupe, A., Navarro, D., Parisi, G., Pérez-Gaviro, S., Pivanti, M., Ricci-Tersenghi, F., Ruiz-Lorenzo, J.J., Schifano, S.F., Seoane, B., Tarancón, A., Tripiccione, R., Yllanes, D., 2014, Phys. Rev. E, (in press) (Preprint arXiv:1307.4998). [35] Belletti, F., Guidetti, M., Maiorano, A., Mantovani, F., Schifano, S.F., Tripiccione, R., Cotallo, M., Pérez Gaviro, S., Sciretti, D., Velasco, J.L., Cruz, A., Navarro, D., Tarancón, A., Fernández, L.A., Martín-Mayor, V., Muñoz-Sudupe, A., Yllanes, D., Gordillo-Guerrero, A., Ruiz-Lorenzo, J.J., Marinari, E., Parisi, G., Rossi, M., Zanier, G., (Janus Collaboration), 2009, Computing in Science and Engineering, 11, 48. [36] Álvarez Baños, R., Cruz, A., Fernández, L.A., Gil-Narvión, J.M., Gordillo-Guerrero, A., Guidetti, M., Maiorano, A., Mantovani, F., Marinari, E., Martín-Mayor, V., Monforte-García, J., Muñoz Sudupe, A., Navarro, D., Parisi, G., Pérez-Gaviro, S., Ruiz-Lorenzo, J.J., Schifano, S.F., Seoane, B., Tarancón, A., Tripiccione, R., Yllanes, D., (Janus Collaboration), 2010, J. Stat. Mech., 2010, P06026 (Preprint arXiv:1003.2569). [37] Baños, R.A., Cruz, A., Fernández, L.A., Gil-Narvión, J.M., Gordillo-Guerrero, A., Guidetti, M., Iñiguez, D., Maiorano, A., Mantovani, F., Marinari, E., Martín-Mayor, V., Monforte-García, J., Muñoz Sudupe, A., Navarro, D., Parisi, G., Pérez-Gaviro, S., Ricci-Tersenghi, F., Ruiz-Lorenzo, J.J., Schifano, S.F., Seoane, B., Tarancón, A., Tripiccione, R., Yllanes, D., 2011, Phys. Rev. B, 84(17), 174209 (Preprint arXiv:1107.5772) URL http://link.aps.org/doi/10.1103/PhysRevB.84.174209. [38] Baity-Jesi, M., Baños, R.A., Cruz, A., Fernández, L.A., Gil-Narvión, J.M., Gordillo-Guerrero, A., Guidetti, M., Iñiguez, D., Maiorano, A., Mantovani, F., Marinari, E., Martín-Mayor, V., Monforte-García, J., Muñoz Sudupe, A., Navarro, D., Parisi, G., Pivanti, M., Pérez-Gaviro, S., Ricci-Tersenghi, F., Ruiz Lorenzo, J.J., Schifano, S.F., Seoane, B., Tarancón, A., Téllez, P., Tripiccione, R., Yllanes, D., 2012, Eur. Phys. J. Special Topics, 210, 33 (Preprint arXiv:1204.4134). [39] Debenedetti, P.G., 1997, Metastable Liquids (Princeton: Princeton University Press). [40] Debenedetti, P.G., Stillinger, F.H., 2001, Nature, 410, 259–267. [41] Cavagna, A., 2009, Physics Reports, 476, 51–124 (Preprint arXiv:0903.4264). [42] Castellani, T., Cavagna, A., 2005, J. Stat. Mech., 2005, P05012. [43] Kirkpatrick, T.R., Thirumalai, D., 1987, Phys. Rev. B, 36, 5388. [44] Kirkpatrick, T.R., Thirumalai, D., Wolynes, P.G., 1989, Phys. Rev. A, 40, 1045. [45] Moore, M.A., Drossel, B., 2002, Phys. Rev. Lett., 89, 217202 (Preprint arXiv:cond-mat/0201107). [46] Fullerton, C.J., Moore, M.A., 2013, (Preprint arXiv:1304.4420). [47] Parisi, G., Ricci-Tersenghi, F., 2012, Phil. Mag. B, 92, 341 (Preprint arXiv:1108.0759v1). [48] Nightingale, M.P., 1975, Physica A, 83, 561. [49] Binder, K., 1982, Phys. Rev. A, 25, 1699. [50] Ballesteros, H.G., Fernández, L.A., Martín-Mayor, V., Muñoz Sudupe, A., Parisi, G., Ruiz-Lorenzo, J.J., 1998, Nucl. Phys. B, 512, 681. [51] Baity-Jesi, M., Baños, R.A., Cruz, A., Fernández, L.A., Gil-Narvión, J.M., Gordillo-Guerrero, A., Iñiguez, D., Maiorano, A., Mantovani, F., Marinari, E., Martín-Mayor, V., Monforte-García, J., Muñoz Sudupe, A., Navarro, D., Parisi, G., Pérez-Gaviro, S., Pivanti, M., Ricci-Tersenghi, F., Ruiz-Lorenzo, J.J., Schifano, S.F., Seoane, B., Tarancón, A., Tripiccione, R., Yllanes, D. (Janus Collaboration), 2013, Phys. Rev. B, 88, 224416 (Preprint arXiv:1310.2910). [52] Baity-Jesi, M., Fernández, L.A., Martín-Mayor, V., Sanz, J.M., 2014, Phys. Rev. B, 89(1), 014202 (Preprint arXiv:1309.1599). [53] Lee, L.W., Young, A.P., 2003, Phys. Rev. Lett., 90, 227203. [54] Jörg, T., 2006, Phys. Rev. B, 73, 224431. [55] Fernández, L.A., Martín-Mayor, V., Yllanes, D., 2009, Nucl. Phys. B, 807, 424–454. [56] Campos, I., Cotallo-Aban, M., Martín-Mayor, V., Pérez-Gaviro, S., Tarancón, A., 2006, Phys. Rev. Lett., 97, 217204. [57] Baños, R.A., Fernández, L.A., Martín-Mayor, V., Young, A.P., 2012, Phys. Rev. B, 86, 134416 (Preprint arXiv:1207.7014). [58] Fernández, L.A., Martín-Mayor, V., Parisi, G., Seoane, B., 2013, EPL, 103, 67003 (Preprint arXiv:1307.2361). [59] Belletti, F., Cruz, A., Fernández, L.A., Gordillo-Guerrero, A., Guidetti, M., Maiorano, A., Mantovani, F., Marinari, E., Martín-Mayor, V., Monforte, J., Muñoz Sudupe, A., Navarro, D., Parisi, G., Pérez-Gaviro, S., Ruiz-Lorenzo, J.J., Schifano, S.F., Sciretti, D., Tarancón, A., Tripiccione, R., Yllanes, D. (Janus Collaboration), 2009, J. Stat. Phys., 135, 1121 (Preprint arXiv:0811.2864). [60] Hukushima, K., Nemoto, K., 1996, J. Phys. Soc. Japan, 65, 1604 (Preprint arXiv:cond-mat/9512035). [61] Marinari, E., 1998, Optimized Monte Carlo methods Advances in Computer Simulation, ed. Kerstész, J. and Kondor, I. (Springer-Berlag). [62] Newman, M.E.J., Barkema, G.T., 1999, Monte Carlo Methods in Statistical Physics (Oxford: Clarendon Press). [63] Fernández, L.A., Martín-Mayor, V., Pérez-Gaviro, S., Tarancón, A., Young, A.P., 2009, Phys. Rev. B, 80, 024422. [64] Yllanes, D., 2011, Rugged Free-Energy Landscapes in Disordered Spin Systems (Ph.D. thesis, UCM) (Preprint arXiv:1111.0266). [65] de Dominicis, C., Giardina, I., 2006, Random Fields and Spin Glasses (Cambridge, England: Cambridge University Press). [66] Amit, D.J., Martín-Mayor, V., 2005, Field Theory, the Renormalization Group and Critical Phenomena 3rd ed (Singapore: World Scientific) URL http://www.worldscientific.com/worldscibooks/10.1142/5715. [67] Ballesteros, H.G., Fernández, L,A,, Martín-Mayor, V., Muñoz Sudupe, A., 1996, Phys. Lett. B, 378, 207 (Preprint arXiv:hep-lat/9511003). [68] Fernández, L.A., Martín-Mayor, V., 2009, Phys. Rev. E, 79, 051109. [69] Álvarez Baños, R., Cruz, A., Fernández, L.A., Gil-Narvión, J.M., Gordillo-Guerrero, A., Guidetti, M., Maiorano, A., Mantovani, F., Marinari, E., Martín-Mayor, V., Monforte-García, J., Muñoz Sudupe, A., Navarro, D., Parisi, G., Pérez-Gaviro, S., Ruiz-Lorenzo, J.J., Schifano, S.F., Seoane, B., Tarancón, A., Tripiccione, R., Yllanes, D. (Janus Collaboration), 2010, Phys. Rev. Lett., 105, 177202 (Preprint arXiv:1003.2943). [70] Hyndman, R., Fan, Y., 1996, American Statistician, 50(4), 361. [71] de Dominicis, C., Kondor, I., Temesvári, T., 1998, Beyond the Sherrington-Kirkpatrick model Spin Glasses and Random Fields, ed. Young, A.P. (Singapore: World Scientific) (Preprint arXiv:cond-mat/9705215). [72] Fisher, K., Hertz, J., 1991, Spin Glasses (Cambridge England: Cambridge University Press). [73] Fisher, D.S., Sompolinsky, H., 1985, Phys. Rev. Lett., 54, 1063.
URI
https://hdl.handle.net/20.500.14352/35124
Collections
Artículos