A scenario for the c<1 barrier in non-critical bosonic strings

The c less than or equal to 1 and c > 1 matrix models are analyzed within the large-N renormalization group taking into account touching (or branching) interactions. The c < 1 modified matrix model with string exponent <(gamma)over bar> > 0 is naturally associated with an unstable fixed point, separating the Liouville phase (gamma < 0) from the branched polymer phase (gamma = 1/2). It is argued that at c = 1 this multicritical fixed point and the Liouville fixed point coalesce, and that both fixed points disappear for c > 1. In this picture, the critical behavior of c > 1 matrix models is generically that of branched polymers, but only within a scaling region which is exponentially small when c --> 1. Large crossover effects occur for c - 1 small enough, with a c similar to 1 pseudo-scaling which explains the numerical results.