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
