Dependence of the surface tension on the shape of surface boundary

• The surface tension of membranes is numerically checked whether it is independent of the shape of surface boundary.
• Monte Carlo simulations are performed on the surfaces with two different boundaries of the same projected area.
• The difference of the surface tension disappears in the thermodynamic limit.
• The Helfrich–Polyakov and Landau–Ginzburg models are simulated.

We numerically check that the surface tension of membranes is independent of the shape of surface boundary. The surface tension is calculated by means of the Monte Carlo simulation technique on two types of cylinders made of rubans of size L1L1 and L2L2, where the rubans are the same for the projected area and different in the ratio L1/L2L1/L2. The difference of the surface tension disappears in the thermodynamic limit in both models of Helfrich–Polyakov and Landau–Ginzburg.