# Magnetic susceptibility vs Monte Carlo step

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?