There is a project I'm working on to model the phase transition of 2 polymers with and without an external E-field. The approach I am taking is first to consider 2 types of dipoles, with a constant external field in the 'up' direction. I'm thinking in two dimensions for now. The dipoles can have 4 orientations and can be next to each other, or on top of one another giving 32 possible configurations. I know this is crying out for a Monte Carlo simulation which is an approach I am also pursuing however I'd like to progress analytically. Having calculated the energies for the 2 cases, next to or on top of, I get 2 partition functions and 2 average energies. I need to combine the two energies to get an overall average which I can work with in Flory theory. This is where I am having trouble.