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 ρ=exp(-κ/k_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 ρ≳ρ_c. For ρ<ρ_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 (ρ=ρ_c), which has a tricritical character, the average radius and the canonical partition function of vesicles with n plaquettes scale as n^ν_c and n^-θ_c, respectively, with ν_c=0.4825±0.0015 and θ_c=1.78±0.03. These exponents indicate a new class, distinct from that of branched polymers, for scaling at the crumpling point. © 1996 The American Physical Society.