Width of handles in two-dimensional quantum gravity

Abstract

We discuss the average length l of the shortest non-contractible loop on surfaces in the two-dimensional pure quantum gravity ensemble. The value of $\gamma_{str}$ and the explicit form of the loop functions indicate that l diverges at the critical point. Scaling arguments suggest that the critical exponent of l is 1/2. We show that this value of the critical exponent is also obtained for branched polymers where the calculation is straightforward.