4-LOOP RESULT IN SU(3) LATTICE GAUGE-THEORY BY A STOCHASTIC METHOD - LATTICE CORRECTION TO THE CONDENSATE

We describe a stochastic technique which allows one to compute numeric ally the coefficients of the weak-coupling perturbative expansion of a ny observable in Lattice Gauge Theory. The idea is to insert the expon ential representation of the link variables U(mu)(x) --> exp{A(mu)(x)/ square-root beta} into the Langevin algorithm and the observables and to perform the expansion in beta-1/2. The Langevin algorithm is conver ted 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.