Crumpling and Buckling Transitions in Polymerized Membranes

We consider polymerized non-self-avoiding membranes fluctuating under constrained boundary conditions. Such constraints prevent the membranes from being crumpled at high temperature and introduce a tension. Upon lowering the temperature this tension reduces, and vanishes at a transition temperature below which the membrane assumes a buckled state. Buckling transition points, depending on boundary conditions, arrange on a line which terminates at the crumpling transition. We study the critical properties of these transitions by various field-theoretical techniques.