Crumpling transition of self-avoiding tethered membranes caused by screening

A system of D-dimensional self-avoiding tethered membranes embedded in a d-dimensional space is considered for the seni-dilute case. The effect of the screening is taken into account, and the crumpled phase diagram in the (d, D) plane is obtained. For D = 2, membranes are in the swollen crumpled phase. The possobility of a crumpling transition caused by the screening is discussed. The density dependences for some quantities such as the screening length and radius of gyration are obtained from a scaling argument.