Biased Monte Carlo algorithms on unitary groups

Michael Creutz; H. Gausterer; S. Sanielevici

doi:10.1103/PhysRevD.39.689

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Biased Monte Carlo algorithms on unitary groups

Michael Creutz, H. Gausterer, and S. Sanielevici

Physics Department, Brookhaven National Laboratory, Upton, New York 11973

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Phys. Rev. D 39, 689 – Published 15 January, 1989

DOI: https://doi.org/10.1103/PhysRevD.39.689

Abstract

We introduce a general updating scheme for the simulation of physical systems defined on unitary groups, which eliminates the systematic errors due to inexact exponentiation of algebra elements. The essence is to work directly with group elements for the stochastic noise. Particular cases of the scheme include the algorithm of Metropolis et al., overrelaxation algorithms, and globally corrected Langevin and hybrid algorithms. The latter are studied numerically for the case of SU(3) theory.

References (13)

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H. Gausterer and S. Sanielevici, Phys. Rev. D 38, 1220 (1988).
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[c1] F. Fucito, E. Marinari, G. Parisi and C. Rebbi, Nucl. Phys. B180, 369 (1981).

[c2] G. G. Batrouni, G. R. Katz, A. S. Kronfeld, G. P. Lepage, B. Svetitsky and K. G. Wilson, Phys. Rev. D 32, 2736 (1985); A. Ukawa and M. Fukugita, Phys. Rev. Lett. 55, 1854 (1985).

[c3] S. Duane, Nucl. Phys. B257, 652 (1985); S. Duane and J. Kogut, Phys. Rev. Lett. 55, 2774 (1985); S. Gottlieb, W. Liu, D. Toussaint, R. L. Renken and R. L. Sugar, Phys. Rev. D 35, 2531 (1987).

[c4] R. Scalettar, D. Scalapino and R. Sugar, Phys. Rev. B 34, 7911 (1986); S. Duane, A. D. Kennedy, B. J. Pendleton and D. Roweth, Phys. Lett. B 195, 216 (1987); M. Creutz, Nucl. Phys. B (Proc. Suppl.) 4, 547 (1988).

[c5] H. Gausterer and S. Sanielevici, Phys. Rev. D 38, 1220 (1988).

[c6] R. Gupta, Nucl. Phys. B (Proc. Suppl.) 4, 562 (1988); R. Gupta, G. W. Kilcup and S. Sharpe, Phys. Rev. D 38, 1278 (1988).

[c7] K. Bitar, A. D. Kennedy, R. Horsley, S. Meyer, and P. Rossi, Report No. FSU-SCRI-88-14, 1988 (unpublished).

[c8] M. Creutz, Phys. Rev. D 38, 1228 (1988).

[c9] S. L. Adler, Phys. Rev. D 23, 2901 (1981).

[c10] F. R. Brown and T. J. Woch, Phys. Rev. Lett. 58, 2394 (1987); M. Creutz, Phys. Rev. D 36, 515 (1987).

[c11] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys. 21, 1087 (1953).

[c12] A. Guha and S. C. Lee, Phys. Rev. D 27, 2412 (1983).

[c13] S. Duane, Nucl. Phys. B257, 652 (1985).

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Biased Monte Carlo algorithms on unitary groups

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