Advertisement

Large Scale Computing in Theoretical Physics: Example QCD

  • K. Schilling
Conference paper

Abstract

The limitations of the classical mathematical analysis of Newton and Leibniz appear to be more and more overcome by the power of modern computers. Large scale computing techniques — which resemble closely the methods used in simulations within statistical mechanics — allow to treat nonlinear systems with many degrees of freedom such as field theories in nonperturbative situations, where analytical methods do fail. The computation of the hadron spectrum within the framework of lattice QCD sets a demanding goal for the application of supercomputers in basic science. It requires both big computer capacities and clever algorithms to fight all the numerical evils that one encounters in the Euclidean world. The talk will attempt to describe both the computer aspects and the present state of the art of spectrum calculations within lattice QCD.

Keywords

Gauge Theory ISING Model Conjugate Gradient Algorithm Lattice Gauge Theory Array Processor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E.Ising: Z.Ph0079s.31 (1925)253ADSCrossRefGoogle Scholar
  2. 2.
    N.Metropolis, A.W.Rosenbaum, M.N.Rosenbluth, A.H.Teller, E.Teller: J.Chem.Phys. 21 (1953)1087ADSCrossRefGoogle Scholar
  3. 3.
    G. Bhanot, D.Duke, R.Salvador: ‘A Fast Algorithm for the CDC Cyber 205 to Simulate 3-d ISING Model, Tallahasse preprint FSÜ-SCRI 86–04Google Scholar
  4. 4a.
    see e.g. K.Binder:in Phase Transitions and Critical Phenomena, C. Domb and M.S. Green, eds., Vol.5B, Academic Press, New York 1976)Google Scholar
  5. 4b.
    and K.Binder(ed.) Monte Carlo Methods, Springer, Berlin-Heidelberg-New York 1979Google Scholar
  6. 5.
    K.G.Wilson: Phys.Rev. D10(1974) 2445ADSGoogle Scholar
  7. 6.
    see e.g. the textbook of C.Itzykson and J.-B. Zuber: Quantum Field Theory McGraw Hill 1980Google Scholar
  8. 7.
    for the history of asymptotic freedom, see G.t’Hooft: Proceedings of the ‘Colloquium in Memoriam Kurt Svmanzik’. held in Hamburg, Febr.1984, North Holland, AmsterdamGoogle Scholar
  9. 8.
    S.Fernbach: Future Generations Computer Systems 1(1984) 23CrossRefGoogle Scholar
  10. 9.
    M.Creutz: Phys.Rev. D21(1980) 2308MathSciNetADSGoogle Scholar
  11. 10.
    for the most recent status,see e.g. the Proceedings of the workshop “Lattice Gauge Theory — A Challenge in Large — Scale Computing”, held in in Wuppertal, Nov.1985, R.Bunk,K.H.Mütter, K.Schilling (eds.), Plenum Press, Lodon-New York 1986 for an introduction, see the lectures of G.Schierholz given at the 27th Summer School of the Scottish Universities in Physics, St.Andrews, August 1984Google Scholar
  12. 11.
    for an introduction see e.g. the textbook of I.J.R Aitchison: An Informal Introduction to Gauge Theories. Cambridge university Press, 1982MATHCrossRefGoogle Scholar
  13. 12.
    see e.g. Prooeedings of the Workshop ‘Advances in Lattice Gauge Theory’, held in Tallahassee, April 1985, World Scientific, Singapore 1985Google Scholar
  14. 13a.
    K.H.Mütter, K.Schilling: Nucl.Phys. B230 (FS10) (1984) 275ADSCrossRefGoogle Scholar
  15. 13b.
    A.König, K.H.Mütter, K.Schilling: Phys.Lett. 147B(1984) 145Google Scholar
  16. 13c.
    A.König, K.H.Mütter, K.Schilling: J.Smit, Phys.Lett. 157B (1985) 421Google Scholar
  17. 14.
    Ph. deForerand, A.König, K.H.Mütter, K.Schilling, R.Sommer, in the Proceedings of the Wuppertal workshop, ibid., R.Sommer, contribution to the 2nd Dutch-German Symposion held in Bad Honnef, April 1986 and Wuppertal preprint WU B 86/12, to be publishedGoogle Scholar
  18. 15.
    R.D.Kenway, in the Proceedings of the Wuppertal workshop, ibid.Google Scholar
  19. 16.
    D.Barkai, K.Moriarty, C.Rebbi, Phys.Lett. 156B(1985) 385ADSGoogle Scholar
  20. 17.
    S.Itoh, Y.Iwasaki, T.Yoshie, Tsukuba preprint UTHEP-155, May 1986Google Scholar
  21. 18.
    J.Kogut, L.Susskind, Phys.Rev D11(1975) 395ADSGoogle Scholar
  22. 19.
    There is a long and still open discussion in the literature about the most efficient algorithm to treat dynamical fermions. We refer the reader to the contributions of J.B.Kogut, G.G.Batrouni, F.Fucito, and D.Weingarten in the Proceedings of the Tallahasse Workshop,ibid.Google Scholar
  23. 20.
    E.Laermann, F.Langhammer, I.Schmitt, and P.M.Zerwas:’, Masses and chiral Symmetry Breaking: SU(2) Cloour Gauge Theory with Dynamical Fermions’, CERN preprint TH 4394/86Google Scholar
  24. 21.
    O.Haan, E.Laermann, K.Schilling, and E.Schnepf: Wuppertal preprint in preparationGoogle Scholar
  25. 22.
    E.Marinari:‘The APE Computer and Lattice Gauge Theories’, in the Proceedings of the Wuppertal workshop, ibid.Google Scholar
  26. 23.
    G.C.Fox, S.W.Otto:‘Caltech Concurrent Computation Program: A Status Report’, Caltech preprint HM 157 B, CALT-68–1317Google Scholar
  27. 24.
    J.Beetem, M.Denneau, D.Weingarten: in the IEEE Proceedings of the 12th International Symposium on Computer Architecture, held in Boston, June 1985Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • K. Schilling
    • 1
  1. 1.University of WuppertalWuppertalF. R. Germany

Personalised recommendations