BENDING-RIGIDITY-DRIVEN TRANSITION AND CRUMPLING-POINT SCALING OF LATTICE VESICLES

The crumpling transition of three-dimensional (3D) lattice vesicles su bject to a bending fugacity rho = exp(- kappa/k(B)T) is investigated b y Monte Carlo methods in a grand canonical framework. By also exploiti ng conjectures suggested by previous rigorous results, a critical regi me with scaling behavior in the universality class of branched polymer s is found to exist for rho > rho(c). For rho < rho(c) the vesicles un dergo a first-order transition that has remarkable similarities to the line of droplet singularities of inflated 2D vesicles. At the crumpli ng point (rho = rho(c)), which has a tricritical character, the averag e radius and the canonical partition function of vesicles with n plaqu ettes scale as n(nu c) and n-(theta c), respectively, with nu(c) = 0.4 825 +/- 0.0015 and theta(c) = 1.78 +/- 0.03. These exponents indicate a new class, distinct from that of branched polymers, for scaling at t he crumpling point.