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Correlation between two variables (or objects) is, very simply put, how much a change in one variable affects or determines a change in the other. Replacing variables with spins, highly correlated spins would mean that, due to some interactions between them, a change in the direction of one spin will cause a change in the direction of the spin it is ...


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Your requirement that $z\to 1$ (i.e. $\mu\to 0$) already requires the limit $N\to \infty$. If $N$ is finite, the chemical potential tends to a small but finite value at the transition temperature. This ensures that the occupation of the ground state is $\langle n_0\rangle \lesssim N$.


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It's not the details of the interaction that provide the clue, it's the cooperativity of the effect. For example, in a ferromagnet, there's no point to any one spin lining up unless its neighbors are aligned. That leads to the abrupt change from no long-range magnetic order to the onset of some long-range magnetic order starting at a well-defined temperature ...


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The obvious order parameter is something like the fraction of atoms or molecules ionized, say "x'. Simple stat mech says that at any finite temperature that will be in the range (0,1). The question is whether, for some density of particles, there's a discontinuity as a function of T in either x (first order) or dx/dT (second order). There's a reason some ...


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If your transition from high order to low order occurs slowly over a large number of lattice periods, then you can try doing a discrete Fourier transform of the area of interest taking some windowing function to focus your the computation to area of interest. Then if you get relatively sharp peaks (up to spectral leakage of the window you chose), the ...


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It's not necessarily incorrect, it depends on the system you're modelling. A change in state is usually associated with a change in pressure. But in experimental situations the pressure is usually constant, which means that the volume of your simulation cell must change (hence you'd require NPT rather than NVT). However, there are scenarios in which phase ...



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