Towards the matrix model of M-theory on a lattice

The Wilson discretization of the dimensionally reduced supersymmetric Yang- Mills theory is constructed. This gives a lattice version of the matrix mod el of M-theory. An SU(2) model is studied numerically in the quenched appro ximation for D = 4. The system shows canonical scaling in the continuum lim it. A clear signal for a prototype of the "black hole to strings" phase tra nsition is found. The pseudocritical temperature is determined and the temp erature dependence of the total size of the system is measured in both phas es, Further applications are outlined.