I am studying the 2D Ising model using Monte Carlo simulations and I have learned the binning (or batching) method for the error statistical analysis. Following this discussion https://books.google.it/books?id=3HIZDAAAQBAJ&pg=PA50&lpg=PA50&dq=montecarlo+method+blocking&source=bl&ots=uGuCoCV02v&sig=ACfU3U1j1IvDhJ9vVhuG9eUfKI0IIWe4Fw&hl=it&sa=X&ved=2ahUKEwjr8t6Fs5bhAhVNsaQKHYPGClgQ6AEwCXoECAkQAQ#v=onepage&q=montecarlo%20method%20blocking&f=false (page 50) I have understood that the error of an observable $X$ is computed through the error of the block averages as $$\text{var}(\overline{X})=\frac{1}{N_{blocks}}\text{var}(\overline{X}_{blocks})$$ Now my problem is the following: if the observable I am interested in is the magnetic susceptibility, which is computed from the magnetisation data as $\chi=\beta\text{var}(m)$, where $m$ is the magnetisation and $\beta$ is the inverse temperature, after having divided the Monte Carlo data into sub-blocks and having found uncorrelated block averages, how do I find the error associated to $\chi$? It seems to be the variance of the variance, but it is non-sense for me. Thank you for the help.


1 Answer 1


Fear not! I think it is possible to take the variance of the variance of the variance.

  • $\begingroup$ But in order to compute the variance you need a set of measures, while here I would have just $\chi$ (which is a variance). So how to compute its variance? $\endgroup$
    – MariNala
    May 13, 2019 at 18:33

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