Critical parameters of the three-dimensional Ising spin glass
| dc.contributor.author | Baity Jesi, Marco | |
| dc.contributor.author | Fernández Pérez, Luis Antonio | |
| dc.contributor.author | Martín Mayor, Víctor | |
| dc.contributor.author | Muñoz Sudupe, Antonio | |
| dc.date.accessioned | 2023-06-19T15:01:45Z | |
| dc.date.available | 2023-06-19T15:01:45Z | |
| dc.date.issued | 2013-12-20 | |
| dc.description | © 2013 American Physical Society. Artículo firmado por 24 autores. The total simulation time devoted to this project was the equivalent of 107 days of the full Janus machine (L 32) and 43 days of the full (3072 cores) Memento cluster. 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 the MICINN (Spain) (Contracts No. FIS2006-08533, No. FIS2012-35719-C02, No. FIS2010-16587, No. TEC2010-19207); by the SUMA project of INFN (Italy); by the Junta de Extremadura (GR10158); by the Microsoft Prize 2007, and by the European Union (PIRSESGA-2011-295302). F.R.-T. was supported by the Italian Research Ministry through FIRB Project No. RBFR086NN1; M.B.-J. was supported by the FPU program (Ministerio de Educación, Spain); R.A.B. and J.M.-G. were supported by the FPI program (Diputación de Aragón, Spain); finally J.M.G.-N. was supported by the FPI program (Ministerio de Ciencia e Innovación, Spain). | |
| dc.description.abstract | We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L = 40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain Tc = 1.1019(29) for the critical temperature, ν = 2.562(42) for the thermal exponent, η = −0.3900(36) for the anomalous dimension, and ω = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield α = −5.69(13), β = 0.782(10), and γ = 6.13(11). We also compute several universal quantities at Tc. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Unión Europea. FP7 | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación (MICINN) | |
| dc.description.sponsorship | EU (FEDER funds) | |
| dc.description.sponsorship | INFN (Italy) | |
| dc.description.sponsorship | Junta de Extremadura (Spain) | |
| dc.description.sponsorship | Microsoft Prize 2007 | |
| dc.description.sponsorship | European Union | |
| dc.description.sponsorship | Italian Research Ministry through FIRB | |
| dc.description.sponsorship | FPU program (Ministerio de Educación, Spain) | |
| dc.description.sponsorship | FPI program (Diputación de Aragón, Spain) | |
| dc.description.sponsorship | FPI program (Ministerio de Ciencia e Innovación, Spain) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/37252 | |
| dc.identifier.doi | 10.1103/PhysRevB.88.224416 | |
| dc.identifier.issn | 1098-0121 | |
| dc.identifier.officialurl | http://doi.org/10.1103/PhysRevB.88.224416 | |
| dc.identifier.relatedurl | http://journals.aps.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/35159 | |
| dc.issue.number | 22 | |
| dc.journal.title | Physical review B | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | CriPheRaSy (247328) | |
| dc.relation.projectID | SPIDER (295302) | |
| dc.relation.projectID | FIS2012-35719-C02 | |
| dc.relation.projectID | FIS2006-08533 | |
| dc.relation.projectID | FIS2010-16587 | |
| dc.relation.projectID | UNZA05-33-003 | |
| dc.relation.projectID | MEC-DGA | |
| dc.relation.projectID | TEC2010-19207 | |
| dc.relation.projectID | SUMA project | |
| dc.relation.projectID | GR10158 | |
| dc.relation.projectID | RBFR086NN1 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 53 | |
| dc.subject.keyword | Monte-Carlo | |
| dc.subject.keyword | Model | |
| dc.subject.keyword | Universality | |
| dc.subject.keyword | Simulations | |
| dc.subject.keyword | Transition | |
| dc.subject.keyword | Systems. | |
| dc.subject.ucm | Física (Física) | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.unesco | 22 Física | |
| dc.title | Critical parameters of the three-dimensional Ising spin glass | |
| dc.type | journal article | |
| dc.volume.number | 88 | |
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Rev. B, 86, 184428 (2012). 48) N. G. Fytas, V. Martín-Mayor, Phys. Rev. Lett., 110, 227201 (2013). 49) Dimensionless quantities behave as a function of L and the reduced temperature t = (T − Tc)/Tc as g(L,t) = f_(g)(L^(1/ν) t) + L^(−ω)h_(g)(L^(1/ν) t) +··· where f_(g) and h_(g) are very smooth (actually analytical) scaling functions. In particular, we name fξ and gξ the scaling functions corresponding to ξ/L. In fact, see, e.g., Ref. 36, the detailed form of Eq. (18) follows from the Taylor expansions fξ(x) = fξ(0)+ xf'ξ(0)+··· and hξ(x)= hξ(0)+··· : t^(cross)_(L,2L) = [(hξ(0))/(f'ξ(0))] [(1 − 2^(−ω)) / (2^(1/ν)−1)] L^(−ω−1/ν) +··· . A similar computation yields the amplitudes for the scaling corrections of g^(cross)_(2L) and g^(cross)_(L) in Eq. (17): A^(2L)_(g) = 2^(1/ν) [(1 − 2^(−ω)) / (2^(1/ν) − 1)] hξ(0) [(f'_(g)(0)) / (f'_(ξ)(0))] + 2^(ω)h_(g)(0),and A^(L)_(g) = [(1 − 2^(−ω)) / (2^(1/ν) − 1)] hξ(0) [(f'_(g)(0)) / (f'_(ξ)(0))] + h_(g)(0). Either of the two amplitudes A(L) g , A(2L) g can dominate, depending both on g and on the magnitude chosen to find the crossing point (ξ/L, U4, etc.). 50) It is important to remark that the parametrization of Eq. (24) contains only the first in an infinite (asymptotic) series of scaling corrections. A somehow paradoxical consequence is that obtaining data on small systems with extremely high accuracy may turn out to be useless, as this would only expose subleading scaling corrections that are difficult to parametrize and control. In any numerical study a tradeoff should be found: for a given statistical accuracy, only data from large enough system sizes, L Lmin, should be kept, so that the leading-order corrections in Eq. (17) are adequate within errors. The larger the accuracy, the larger the necessary Lmin. 51) D. Yllanes, Rugged Free-Energy Landscapes in Disordered Spin Systems (Ph.D. thesis, Universidad Complutense de Madrid, 2011), arXiv:1111.0266. 52) As usual, β = 1/T . We employ it in order to allow for a direct comparison with raw data from Ref. 24. | |
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