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It is important to note that there are two different boundary conditions, the first is the boundary condition for real spin model, the second is for fermion model. In fact, for real spin model with a certain boundary condition, there may be different corresponding boundary conditions for fermion operator. When we make a simulation in reality, we need to deal ...


The criterion for determining whether mean-field theory is good or not is the Ginzburg criterion. You can estimate how accurate mean-field theory is by computing the leading corrections to it. In particular, the exact Ising model is $$ H = -J \sum_{\langle i j \rangle} s_i s_j, $$ and mean-field theory is done by taking $$ s_i s_j = M^2 + M (s_i + s_j) + (...


I agree your proposed prescription for periodic BC makes sense.

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