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Suppose we have a graph $G$ with $n$ vertices, edgeset $E$, $\mathcal{X}=\{1,-1\}^n$. The partition function of the spin-1/2 Ising model on $G$ is $$Z(J,h)=\sum_{x\in \mathcal{X}} \exp\left(J \sum_{(...

I'm writing with respect to the paper Khatun, Dutta, and Tarafdar - "Islands in Sea" and "Lakes in Mainland" phases and related transitions simulated on a square lattice. Here's a link to a PDF ...