DILUTE AND SEMIDILUTE SOLUTIONS OF RANDOMLY POLYMERIZED MEMBRANES

We present a statistical mechanics of D-dimensional self-avoiding tethered membranes with disorders in d-dimensional space. Using the variational method, we investigate the properties of dilute and semi-dilute solutions. With an assumption of the replica symmetry, we obtain the saddle point equations which contain the screening effects. In the semi-dilute density the renormalized interaction is characterized by the screening length. The crumpled and the crumpled glass phases are considered. For d < 4 and semi-dilute case, the membranes are more crumpled than the membranes with no disorder. The phase diagrams of the crumpled and crumpled glass phases in (d, D) planes are obtained for both densities. Using a scaling argument, we find the density dependencies of physical quantities, such as radius of gyration, screening length and osmotic pressure.