Monte Carlo simulations of branched polymer surfaces without bending elasticity

We study a model of elastic surfaces that was first constructed by Baillie et al. for an interpolation between the models of fluid and crystalline membranes. The Hamiltonian of the model is a linear combination of the Gaussian energy and a squared scalar curvature energy. These energy terms are discretized on dynamically triangulated surfaces that are allowed to self-intersect. We confirm that the model has not only crumpled phases but also a branched polymer phase, and find that the model undergoes a first-order phase transition between the branched polymer phase and one of the crumpled phases. We find also that the model undergoes a second- (or higher-) order phase transition between the branched polymer phase and another crumpled phase.