PERCOLATION ON STRINGS AND THE COVER-UP OF THE C = 1 DISASTER

We study percolation on the worldsheets of string theory for c = 0, 1/2, 1 and 2. For c < 1 we find that critical exponents measured from simulations agree quite well with the theoretical values. For c = 1 we show how log corrections determined from the exact solution reconcile numerical results with the KPZ predictions. We extend this analysis to the large c regime and estimate how finite-size effects will effectively raise the ground-state energy, masking the presence of the tachyon for moderate values of c > 1. It thus appears likely that simulations for c = 2, 3... on numerically accessible lattices will fail to capture even the qualitative behavior of the continuum limit.