Renormalizing the renormalization group pathologies

We review the status of the "pathologies" of the Renormalization Group (RG) encountered when one tries to define rigorously the RG transformation as a map between Hamiltonians. We explain their origin and clarify their status by relating them to the Griffths' singularities appearing in disordered sy stems; moreover, we suggest that the best way to avoid those pathologies is to use the contour representation rather than the spm representation for l attice spin models at low temperatures. Finally, we outline how to implemen t the RG in the contour representation. (C) 2001 Elsevier Science B.V. All rights reserved.