We start by considering a simple cubic lattice system with nearest neighbour interactions under an external field ψ. An example of a 4×4 system is illustrated by Fig. , where its sites are labelled between 1-16. Each site can be occupied by either a fluid particle (gray), a solid particle (red), or being empty. Pair-wise interactions between site 3 and 7, 7 and 11 are included as we only consider nearest neighbour interactions. Therefore, the Hamiltonian for a two-component system with fluid species A and B in an external field ψ can be written as