Non-ergodicity in lattice Monte Carlo simulation of a self-assembling process

Recent works on the lattice Monte Carlo simulation are considerably concerned with microemulsion systems (systems containing oil, surfactant and water). Because of the role of these systems in the industry, the study of these systems is important from theoretical, simulation and experimental points of view. Some authors have used the simplest potential model (considering only hydrophobic interactions) in their papers. In this Letter, it is shown that how these systems are encountered with non-ergodicity. To investigate ergodicity, simulations are run in the canonical ensemble using simple cubic lattice with reptation and configurational bias Monte Carlo moves. Periodic boundary condition and excluded volumes are used to mimic the box of the simulation to the bulk of solution. Results show that in some cases non-ergodicity deviates true ensemble averaging.