I've successfully doing the simulation of Ising Model by Monte Carlo Method. The method that I used is the Wolff Algorithm. Now, I have serval problems. The first one is the error bar estimation . Due to the sample that I obtained in the Markov Chain is correlated, but I really don't understand how to calculated the error bar. When I try to google it, there so many different method including autocorrelation, spin-spin correlation... In my algorithm, once the cluster was updated, I will save it into the cell. How can I use these samples to estimate the error? (if you can show a simple example to illustrate, I will be really appreciated) Besides I don't know how to calculated the correlation function of my system. There were so many different equation used different parameter to calculate the correlation function, I don't know which one I should use.

In my algorithm, Once the system was updated ( A cluster of spin was flipped), I would calculate the magnetisation of the system and stored into the cell. Therefore the number of sample I obtained is equal to the number of Monte Carlo steps. Finally I will take the average of all my sample as a data of the magnetisation in specific temperature. How can I calculate the error in this sample?