I have some difficulties in understanding how to compute the magnetic susceptibility from a Monte Carlo simulation of the Ising model. I know that it is related to the magnetisation of the system by $\chi=\beta \text{Var(m)}$ so it seems that I need to compute the magnetisation over a complete simulation, keep all the values into a vector, and finally compute the variance of that set of measurements.

But what if I would like to compute the magnetic suscpetiblity as a function of the Monte Carlo step? In fact, my goal is to show that after a thermalisation period all the physical observables reach their own equilibrium value. So I would like to plot $\chi$ versus the Monte Carlo step and see how many iterations I need in order to have a stable value for $\chi$.

But if I try to save every consecutive measurements of $m$ and at each step compute $\text{Var(m)}$, I end up with a wrong plot. Where is the conceptual error?


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