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.

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

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• Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions
• A percolation transition in Yang-Mills matter at finite number of colours
• Site Percolation on Planar ${\Phi }^3$ Random Graphs
• Complex Structures Defined on Dynamically Triangulated Surfaces