It depends on where you are heading to.
PhD is a TRAINING which teaches you (well, nobody teaches you anything, you yourself have to learn, follow Phd commics for reference ;)) how to do research, nothing more generally, though there are exceptional people who have done original resaerch...
What is your long term career goal ? A R&D job or a non R&D job ? If non R&D job, then techincal or non-technical ? Which country are you from - a 1st world or 3rd world one? The answer depends on many factors like these. The more detail you provide, better is the answer.
The shortest answer is...
>> $$ E = -\sum_{<ij>}J_{ij}(s_i,s_j)s_is_j $$
Yes, this is better representation.
>> This is an Ising model for a binary system.
Yes, you are right.
>> But you have not specified your boundary conditions.
Yes, I am using periodic boundary condition in all directions.
Thanks...
In the well known Ising model, without any external field (H=0), the energy (E), spins (s) and exchange interaction (J) are related as in the following equation
$$
E = -\sum_{<ij>}J_{ij}s_{i}s_{j}
$$
Jij is site dependent and consists of three components JAA, JBB and JABwhere A is say up...