Abstract
We present an exact solution of the O(n) model on a random lattice. The coupling constant space of our model is parametrized in terms of a set of moment variables and the same type of universality with respect to the potential as observed for the one-matrix model is found. In addition we find a large degree of universality with respect to n; namely for n gE ] - 2,2[ the solution can be presented in a form which is valid not only for any potential, but also for any n (not necessarily rational). The cases n = ±2 are treated separately. We give explicit expressions for the genus-zero contribution to the one- and two-loop correlators as well as for the genus-one contribution to the one-loop correlator and the free energy. It is shown how one can obtain from these results any multi-loop correlator and the free energy to any genus and the structure of the higher-genera contributions is described. Furthermore we describe how the calculation of the higher-genera contributions can be pursued in the scaling limit.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Nuclear Physics B |
| Vol/bind | 455 |
| Udgave nummer | 3 |
| Sider (fra-til) | 577-618 |
| Antal sider | 42 |
| ISSN | 0550-3213 |
| DOI | |
| Status | Udgivet - 27 sep. 1995 |