Percolation on Strings and the Cover-up of the c=1 Disaster

Abstract

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 $c=2,3\dots$ on numerically accessible lattices will fail to even capture the qualitative behavior of the continuum limit.

Comments: revised version w/ typos corrected, standard latex w/ epsf, 9 figures