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 \ensuremath{\rho}=exp(-\ensuremath{\kappa}/${\mathit{k}}_{\mathit{BT}}$) 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.