Phase transition of a model of crystalline membrane

We study two-dimensional triangulated surfaces of sphere topology by the canonical Monte Carlo simulation, The coordination number of surfaces is made as uniform as possible. The triangulation is fixed in MC so that only the positions X of vertices may be considered as the dynamical variable. The well-known Helfrich energy function S = S-1 + bS(2) is used for the definition of the model where S-1 and S-2 are the area and bending energy functions respectively and b is the bending rigidity. The discretizations of S-1 and S-2 are identical with that of our previous MC study for a model of fluid membranes. We find that the specific heats have peaks at finite bending rigidities and obtain the critical exponents of the phase transition by the finite-size scaling technique. It is found that our model of crystalline membranes undergoes an expected second order phase transition.