The crumpling transition of three-dimensional (3D) lattice vesicles subject to a bending fugacity \ensuremath{\rho}=exp(-\ensuremath{\kappa}/kBT​) 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 \ensuremath{\rho}\ensuremath{\gtrsim}{\mathrm{\ensuremath{\rho}}}_{\mathit{c}}. For \ensuremath{\rho}{\mathrm{\ensuremath{\rho}}}_{\mathit{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 (\ensuremath{\rho}={\mathrm{\ensuremath{\rho}}}_{\mathit{c}}), which has a tricritical character, the average radius and the canonical partition function of vesicles with n plaquettes scale as {\mathit{n}}^{{\ensuremath{\nu}}_{\mathit{c}}} and {\mathit{n}}^{\mathrm{\ensuremath{-}}{\mathrm{\ensuremath{\theta}}}_{\mathit{c}}}, respectively, with {\ensuremath{\nu}}_{\mathit{c}}=0.4825\ifmmode\pm\else\textpm\fi{}0.0015 and {\mathrm{\ensuremath{\theta}}}_{\mathit{c}}=1.78\ifmmode\pm\else\textpm\fi{}0.03. These exponents indicate a new class, distinct from that of branched polymers, for scaling at the crumpling point. \textcopyright{} 1996 The American Physical Society
