Exact solution of the O(n) model on a random lattice
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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.
Original language | English |
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Journal | Nuclear Physics B |
Volume | 455 |
Issue number | 3 |
Pages (from-to) | 577-618 |
Number of pages | 42 |
ISSN | 0550-3213 |
DOIs | |
Publication status | Published - 27 Sep 1995 |
ID: 186918844