Approaches to scale invariance in two dimensional statistical mechanics

The field theory limit of critical q = 4 cos2(π/r) (r is an element of Z) state Potts and related models is a Conformal Field Theory (CFT) with central charge c = 1 - 6/r(r - 1). This may be shown by considering charged Coulomb gas models which are known to be universal with the Potts models. The arguments, however, are tortuous. We find vestigial properties in the Potts models associated with the CFT limit directly by mans of block spin transformations. These are motivated by cabling transformations of braids, which arise in the transfer matrix formulation of such models. (author)