Four Loop Result in $SU(3)$ Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate

Details Four Loop Result in $SU(3)$ Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate Four Loop Result in $SU(3)$ Lattice Gauge Theory by a Stochastic Method: Lattice Correction to the Condensate

1994-05-24

arxiv.org/abs/hep-lat/9405019v1

Nucl.Phys. B426 (1994) 675-685

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages. + 5 figures (postscript) appended at the end, (University of Parma, Dept.of Physics, report uprf-397-1994)

Scientific paper

10.1016/0550-3213(94)90026-4

We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the link variables $U_\mu(x) \to \exp\{A_\mu(x)/\sqrt\beta\}$ into the Langevin algorithm and the observables and to perform the expansion in \beta^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of maps which can be exactly truncated at any order. We give the result for the simple plaquette of SU(3) up to fourth loop order (\beta^{-4}) which extends by one loop the previously known series.

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