Phases of a Stack of Membranes at Large-d

The phase diagram of a stack of tensionless membranes with nonlinear curvature energy and vertical harmonic interaction is calculated exactly in a large number of dimensions of configuration space. At low temperatures, the system forms a lamellar phase with spontaneously broken translational symmetry in the vertical direction. At a critical temperature, the stack disorders vertically in a melting-like transition. The critical temperature is determined as a function of the interlayer separation l.