Bending-rigidity-driven transition and crumpling-point scaling of lattice vesicles

The crumpling transition of three-dimensional (3D) lattice vesicles subject to a bending fugacity rho = exp(- kappa/k(B)T) is investigated by Monte Carlo methods in a grand canonical framework. By also exploiting conjectures suggested by previous rigorous results, a critical regime with scaling behavior in the universality class of branched polymers is found to exist for rho > rho(c). For rho < rho(c) the vesicles undergo a first-order transition that has remarkable similarities to the line of droplet singularities of inflated 2D vesicles. At the crumpling point (rho = rho(c)), which has a tricritical character, the average radius and the canonical partition function of vesicles with n plaquettes scale as n(nu c) and n-(theta c), respectively, with nu(c) = 0.4825 +/- 0.0015 and theta(c) = 1.78 +/- 0.03. These exponents indicate a new class, distinct from that of branched polymers, for scaling at the crumpling point.