Abstract
Monte-Carlo renormalization-group methods are formulated for the lattice gauge theory following earlier ideas of Ma and Swendson in statistical mechanics. Expectation values of gauge loops and “block gauge loops” have been computed numerically by Monte-Carlo methods on lattices of maximum size 8 × 8 × 8 × 8. The expectation values of block gauge loops are used to determine the dependence of the bare coupling of the lattice theory on the lattice spacing. The lattice Lagrangian used in the renormalization calculations contained three different loops with coefficients in a fixed ratio. The calculations reported here are preliminary and the renormalization calculation is complete only for one value of the coupling constant. Some simple loop expectation values for the simple plaquette Lagrangian are also reported; similar results have previously been reported by Creutz.
Supported in part by the National Science Foundation
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References
M. Creutz, L. Jacobs and C. Rebbi, Phys. Rev. Lett. 42, 1390 (1979); Phys. Rev. D (to be published).
M. Creutz, Phys. Rev. Lett. 43, 553 (1979).
R.H. Swendson, Phys. Rev. B 20, 2080 (1979)
H.W.J. Blöte and R.H. Swendson, Phys. Rev. B 20, 2077 (1979)
S. Ma, Phys. Rev. Lett. 37, 461 (1976).
See, e.g., A. Peterman, Phys. Reports 53, 159 (1979).
See, e.g., K. Wilson, Phys. Rev. D 10, 2445 (1974)
K. Wilson, in: New Developments in Quantum Field Theory and Statistical Mechanics, (Plenum Press, New York, 1977 ).
Th. Niemeijer and J.M.J. Van Leeuwen, In: Phase Transitions and Critical Phenomena, eds. C. Domb and M.S. Green, ( Academic Press, N.Y., 1976 ), Vol. 6, p. 425.
See, e.g., K. Wilson, Rev. Mod. Phys. 47, 773 (1975).
See, e.g., J.M. Hammersley and D.C. Handscomb, Monte Carlo Methods, (Wiley, New York, 1964).
J.B. Kogut, R.B. Pearson and J. Shigemitsu, Phys. Rev. Lett. 43, 484 (1979).
M. Creutz, Solving Quantized SU(2) Gauge Theory, Brookhaven preprint (1979).
W. Feller, An Introduction to Probability Theory and its Applications, (Wiley, New York, 1966 ) Vol. II, p. 26–488.
D.E. Knuth, The Art of Computer Programming,(Addison-Wesley, Reading, Mass, 1969), Vol.II, Chap.3.
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© 1980 Plenum Press, New York
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Wilson, K.G. (1980). Monte-Carlo Calculations for the Lattice Gauge Theory. In: Hooft, G., et al. Recent Developments in Gauge Theories. NATO Advanced Study Institutes Series, vol 59. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-7571-5_20
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DOI: https://doi.org/10.1007/978-1-4684-7571-5_20
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