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Currently, I did a Monte Carlo simulation with the local update and Wolff cluster updated in 2D classical Ising model. I use the autocorrelation function to compare 2 different algorithm in critical temperature (T ~ 2.269). Thats what I got.enter image description here Is it correct? The local updated algorithm didn't show the exponential decay in the beginning. And it will become negative as it pass through 0. What I expect is that it has an exponential decay in the beginning and fluctuate around 0 once the sample become decorrelated. The equation I used to evaluate the autocorrelation function is enter image description here

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Close to the critical point the dynamics slows down sensibly and power laws start appearing in both structural and dynamical quantities. Therefore, you should not expect simple exponentials when you are close to criticality. Try to run some simulations away from $T_c$ (say, $T = 3$).

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  • $\begingroup$ Or just increase the number of performed moves by a factor of 100/1000. But it is true that several exponential like factors, higher order corrections will appear, and it can be even negative for a short time, before it settles. $\endgroup$
    – Kregnach
    Aug 16, 2021 at 0:25

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