2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192055There exist lattice actions which give cut--off independent physical predictions even on coarse grained lattices. Rotation symmetry is restored, the spectrum becomes exact and, in addition, the classical equations have scale invariant instanton solutions. This perfect action can be made short ranged. It can be determined by combining analytical calculations with numerical simulations on small lattices. We illustrate the method and the benefits on the $d=2$ non--linear $σ$--model.29 pages(part 1) + 9 postscript figures(part 2, compressed by uufiles). No changes, replaced due to transmission error observed, BUTP-93/17High Energy Physics - Latticetext