2008/07/29 by Stecki, J.
#FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.0807.4593
The distinction between the true total area and the projected area is elucidated with soluble models which represent the membrane as a self-avoiding string on a plane. Constraining the total area to a predetermined value changes the averages very significantly. The latter are calculated exactly from the generating functions of self-avoiding walks and are shown as functions of activities q and r related to temperature T=± 1/log (q) and lateral force f=-log (r). The constraint makes the partition functions and averages valid for all q,r >0 and reduces the ratio of Atot to the projected area L. High temperature divergences are supressed. Possible applications to simulated bilayers/membranes are discussed.