# Magnetic susceptibility error by binning Monte Carlo

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.

• 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? – MariNala May 13 at 18:33