The dilute Potts model on random surfaces

摘要

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. Thr method can be equally weil applied to a more general (Q + 1)-matrix model which represents the dilute Ports model on random dynamical lattices. We discuss in particular duality of boundary conditions for open random surfaces. [References: 25]