Additional peaks in the cluster size distribution of amphiphile + water systems: a clue for shape/phase transition or statistical uncertainty

In some works on the lattice Monte Carlo simulation of amphiphilic systems additional peaks in the cluster size distribution has been interpreted as a clue for the phase or shape transition of micellar aggregates. On the other hand, some other works showed that the additional peaks are a result of finite size of the lattice box. In this paper using calculating energy-auto-correlation function and statistical error in correlated data, it is shown that how these apparently contradictory results are the same. To do this, we have simulated a pure system containing amphiphile and water molecules. A simple model of potential containing the main feature for these systems (the hydrophobicity of surfactant molecules) that cause the aggregates to be formed is considered to avoid any synthetic results due to additional non-real parameters. To relax the initial configuration faster, configurational bias Monte Carlo move is used in addition to reptation move. Periodic boundary condition and self-avoiding walks are used as former published works in this field. It is shown that the additional peaks is a result of the statistical errors for averaged cluster size distribution and can not be interpreted as a clue for shape or phase transition.