Melting behavior of an idealized membrane model

Abstract

The melting behavior of an idealized model giving rise to two-dimensional (2D) structures at low temperature and low density is investigated by Monte Carlo simulations. The system is made of particles carrying a spin of constant length and variable orientation, whose potential energy is the sum of a repulsive spherical pair interaction, and of a spin-spin contribution, reminiscent of but essentially different from the electrostatic dipole-dipole interaction. The simulation results show that the model phase diagram is determined by the interplay of a ferro- to paraelectric transition in the spin part and of the solid to fluid transition found in simple pair-potential models. The 2D solid melts into a three-dimensional (3D) fluid when the spin-spin interaction is weak. Strong spin-spin interactions give rise to two transitions, the first one corresponding to the melting of the 2D solid into a 2D fluid, and the second one corresponding to the crossover from a 2D to a 3D fluid. The fluid phase stable in between these two transitions provides a model for the liquid state arising in organic and biological membranes across their main transition.