1999/03/31 by P. Zinn-Justin · 1 citation
Physics and Astronomy · #cond-mat.stat-mech
published as J.Statist.Phys. 98 (2001) 245-264 · 18 pages, 5 EPS figures, lanlmac
arxiv created 1999/04/27 · arxiv updated 2009/11/30
We present a new solution of the asymmetric two-matrix model in the large N limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with the topology of the sphere (resp. the disk) for closed (resp. open) surfaces; we elaborate on the resulting phase diagram. The method can be equally well applied to a more general (Q+1)-matrix model which represents the dilute Potts model on random dynamical lattices. We discuss in particular duality of boundary conditions for open random surfaces.