We present the results of a high statistics lattice study of the gluon propagator, in the Landau gauge, at β = 6.0. As suggested by previous studies, we find that, in momentum space, the propagator is well described by the expression G(k 2 ) = M 2 + Z · k 2 (k 2 /Λ 2 ) η −1 . By comparing G(k 2 ) on different volumes, we obtain a precise determination of the exponent η = 0.532(12), and verify that M 2 does not vanish in the infinite volume limit. The behaviour of η and M 2 in the continuum limit is not known, and can only be studied by increasing the value of β.

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 µ (x) → exp{A µ (x)/ √ β} into the Langevin algorithm and the observables and to perform the expansion in β − 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 (β −4 ) which extends by one loop the previously known series. * Research partially supported by murst, Italy.

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