Layer-by-layer ordering of ultrathin liquid crystal films on the three-level Potts model

The three-level Potts model with variable coupling strengths is proposed to describe the newly observed smectic-A^l to smectic-A phase transition in free-standing liquid crystal films. In a film of L molecular layers, the transition temperature for individual layers is determined separately by the bifurcation point of the free energy in the variational cumulant expansion (VCE), from which the heat capacity is also calculated analytically. By adjusting the interlayer and intralayer coupling between nearest-neighboring molecules, it is shown that the calculated heat capacity qualitatively reproduces the observed anomaly around transition temperatures in experiments on free-standing 54COOBC films of two and more molecular layers.