The $O(n)$ model on a random surface: critical points and large order behaviour

Details The $O(n)$ model on a random surface: critical points and large order behaviour The $O(n)$ model on a random surface: critical points and large order behaviour

1992-04-24

arxiv.org/abs/hep-th/9204082v1

Nucl.Phys. B386 (1992) 558-591

Physics

High Energy Physics

High Energy Physics - Theory

33 pages

Scientific paper

10.1016/0550-3213(92)90630-T

In this article we report a preliminary investigation of the large $N$ limit of a generalized one-matrix model which represents an $O(n)$ symmetric model on a random lattice. The model on a regular lattice is known to be critical only for $-2\le n\le 2$. This is the situation we shall discuss also here, using steepest descent. We first determine the critical and multicritical points, recovering in particular results previously obtained by Kostov. We then calculate the scaling behaviour in the critical region when the cosmological constant is close to its critical value. Like for the multi-matrix models, all critical points can be classified in terms of two relatively prime integers $p,q$. In the parametrization $p=(2m+1)q \pm l$, $m,l$ integers such that $0

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