Monte Carlo simulations of two-dimensional fluid membranes (model of fixed triangulation)

We study numerically a model of fluid membrane with fixed triangulation, where the number of bonds per molecule is made as uniform as possible. The action of the model is dependent on the triangulation of surfaces. We pay special attention to whether or not the observables are dependent on the triangulation at the critical point of the second-order phase transition. By making use of different triangulated surfaces, we observe that the specific heat is divergent at the critical point and that the observables of the model seem to be independent of the triangulations. From the peak height of the specific heat, we obtain a critical exponent of the phase transition. We see that the critical exponents of the models of fixed triangulation and of the dynamical one are not identical.