Widom lattice model statistical mechanics
Lattice sites (here hexagonal) are either hydrophobic or hydrophilic (- or +, black or blue). Amphiphile species are assumed to be present along any juxtaposition of sites with different hydrophobicity, and to be aligned correctly: all other configurations are too high in energy to warrant consideration in a first approximation model. The free energy is the sum of local site contributions.
The ensemble chosen is grand canonical - there is assumed to be a reservoir of water, oil and amphiphiles and their chemical potentials give rise to local entropy terms S, depending on z1 and z2. The Widom energies weight configurations according to the number of pairs of amphiphiles (spin triples +-+ pr -+- at the site).