Mean-value identities as an opportunity for Monte Carlo error reduction
| dc.contributor.author | Fernández Pérez, Luis Antonio | |
| dc.contributor.author | Martín Mayor, Víctor | |
| dc.date.accessioned | 2023-06-20T04:13:54Z | |
| dc.date.available | 2023-06-20T04:13:54Z | |
| dc.date.issued | 2009-05-11 | |
| dc.description | © 2009 The American Physical Society. We acknowledge partial financial support from Ministerio de Ciencia e Innovación Spain through research Contract No. FIS2006-08533. | |
| dc.description.abstract | In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministerio de Ciencia e Innovación, Spain | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/37898 | |
| dc.identifier.doi | 10.1103/PhysRevE.79.051109 | |
| dc.identifier.issn | 1539-3755 | |
| dc.identifier.officialurl | http://doi.org/10.1103/PhysRevE.79.051109 | |
| dc.identifier.relatedurl | http://journals.aps.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/45070 | |
| dc.issue.number | 5 | |
| dc.journal.title | Physical review E | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | FIS2006-08533 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 53 | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Ising-model | |
| dc.subject.keyword | Critical exponents | |
| dc.subject.keyword | Spin-glass | |
| dc.subject.keyword | Algorithm. | |
| dc.subject.ucm | Física (Física) | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.unesco | 22 Física | |
| dc.title | Mean-value identities as an opportunity for Monte Carlo error reduction | |
| dc.type | journal article | |
| dc.volume.number | 79 | |
| dcterms.references | 1) D. P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge University Press, Cambridge), 2000. 2) A. D. Sokal, in Functional Integration: Basics and Applications (1996 Cargèse School), edited by C. DeWitt Morette, P. Cartier, and A. Folacci (Plenum, New York), 1997. 3) G. Parisi, R. Petronzio, F. Rapuano, Phys. Lett. B, 128, 418, 1983. 4) M. Lüscher, P. Weisz, J. High Energy Phys., 09, 2001 010. 5) See, e.g., F. Belletti et al. (the Janus Collaboration), Phys. Rev. Lett., 101, 157201, 2008. 6) J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods (Fletcher and Son, Methuen, London), 1964. 7) R. Y. Rubinstein, Simulation and the Monte Carlo Method (Wiley and Sons, New York), 1981. 8) J. S. Schwinger, Proc. Natl. Acad. Sci. U.S.A., 37, 452, 1951 -- F. J. Dyson, Phys. Rev., 75, 1736, 1949. 9) H. B. Callen, Phys. Lett., 4, 161, 1963. 10) F. Guerra, Int. J. Mod. Phys. B, 10, 1675, 1996. 11) R. H. Swendsen, J. S. Wang, Phys. Rev. Lett., 58, 86, 1987. 12) J. Salas, A. D. Sokal, J. Stat. Phys., 98, 551, 2000. 13) E. Marinari, G. Parisi, J. J. Ruiz-Lorenzo, Phys. Rev. B, 58, 14852, 1998. 14) H. G. Katzgraber, M. Palassini, A. P. Young, Phys. Rev. B, 63, 184422, 2001. 15) See, e.g., H. G. Ballesteros, V. Martín-Mayor, Phys. Rev. E, 58, 6787, 1998, and references therein. 16) H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, Phys. Lett. B, 387, 125, 1996 -- H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, J. J. Ruiz-Lorenzo, Phys. Rev. B, 58, 2740, 1998. 17) M. Weigel, W. Janke, Phys. Rev. Lett., 102, 100601, 2009. 18) For disordered systems, the time average in Eq. (9 is followed by a disorder average, which strongly diminishes the influence of the particular Monte Carlo dynamics). 19) D. Amit, V. Martín-Mayor, Field Theory: The Renormalization Group and Critical Phenomena, 3rd ed. (WorldScientific, Singapore), 2005. 20) S. S. Lavenberg, P. D. Welch, IBM Corporation, Yorktown Heights, New York Research Report No. RC8161, 1980 (unpublished). 21) A. E. Ferdinand, M. E. Fischer, Phys. Rev., 185, 832, 1969. 22) F. Cooper, B. Freedman, D. Preston, Nucl. Phys. B, 210, 210, 1982. 23) L. A. Fernández, V. Martín-Mayor, D. Yllanes, Nucl. Phys. B, 807, 424, 2009. 24) L. A. Fernández, V. Martín-Mayor, S. Pérez-Gaviro, A. Tarancón, A. P. Young e-print arXiv:0905.0322. 25) X. J. Li, A. D. Sokal, Phys. Rev. Lett., 63, 827, 1989. 26) R. G. Edwards, A. D. Sokal, Phys. Rev. D, 38, 2009, 1988. | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication | 061118c0-eadf-4ee3-8897-2c9b65a6df66 | |
| relation.isAuthorOfPublication.latestForDiscovery | 146096b1-5825-4230-8ad9-b2dad468673b |
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