arXiv subjects
Publications and source records attributed to Martin G. Harris.
We show how to determine the unknown functions arising when the peeling decomposition is applied to multi-critical matter coupled to two-dimensional quantum gravity and compute the loop-loop correlation functions. The results that $η=2+2/(2K-3)$ and $ν=1-3/2K$ agree with the slicing decomposition, and satisfy Fisher scaling.
We calculate the Hausdorff dimension, $d_H$, and the correlation function exponent, $η$, for polymerized two dimensional quantum gravity models. If the non-polymerized model has correlation function exponent $η_0 >3$ then $d_H=γ^{-1}$ where $γ$ is the susceptibility exponent. This suggests that these models may be in the same universality class as certain non-generic branched polymer models.
We consider a model of p independent Ising spins on a dynamical planar phi-cubed graph. Truncating the free energy to two terms yields an exactly solvable model that has a third order phase transition from a pure gravity region (gamma=-1/2) to a tree-like region (gamma=1/2), with gamma=1/3 on the critical line. We are able to make an order of magnitude estimate of the value of p above which there exists a branched polymer (ie tree-like) phase in the full model, that is, p is approximately 13-23, which corresponds to a central charge c of about 6-12.