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It is only exactly at the critical temperature that this CFT result works. You haven't mentioned if you have used the critical temperature when you did the monte-carlo. At/near critical point, autocorrelation time becomes huge. (If I am not mistaken, autocorrelation time must blow up exactly at critical temperature, however it is cut-off due to finiteness ...

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A definitive volume, one that I learned from during graduate school, is Kerson Huang's (of MIT, emeritus of the Physics Dept.) Statistical Mechanics. The book covers both classical and quantum computations of the partition function and observables from it, as well as thermodynamics, kinetic theory, transport, superfluids, critical phenomena, and the Ising ...

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I suggest you: Statistical Mechanics: Theory and Molecular Simulation Mark E. Tuckerman There are all the necessary prerequisites and the discussion about Ising model and critical points. I don't know if there's online.

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As in your question the stress was on the word general, I have some bad news: an efficient "general solver (or a theoretical algorithm) for (...) extended Ising models, which involves an arbitrary lattice" does not exists. Of course, one can invent algorithms that, in principle, could find the ground state. The most trivial would be checking the energy of ...

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