Statistical mechanics of three-dimensional vesicles

We consider a lattice model of three-dimensional vesicles in which the boundary of the vesicle is a self-avoiding plaquette surface, homeomorphic to a sphere. Surfaces with fixed area can enclose a variety of different volumes and we associate a fugacity with the enclosed volume to mimic the effect of a pressure difference across the surface. Pairs of plaquettes which share a common edge can be in the same plane or normal to each other and we associate a fugacity with adjacent pairs of plaquettes at right angles to represent a surface stiffness term. We discuss the behaviour of the surfaces in the infinite surface area limit, as a function of these two fugacities.