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I am using the Monte-Carlo metropolis algorithm to simulate the Ising model. Since the convergence is slow near $T_c$, I am looking for a method to speed up the problem. What I did was instead of evaluating the algorithm one site at a time, I am doing it for all sites simultaneously in each iteration. Is this a valid method?

EDIT: What I observe is that the the algorithm converges to the half-full lattice (density = 0.5) at temperatures above $T_c$. Some figures are drawn below:

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As we can see, there is a horizontal line that we do not expect. What is causing it?

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  • $\begingroup$ This is a valid perturbation of the state in the MCMC framework, but it is possible that you get very low acceptance rates. What do you observe? $\endgroup$ May 15 at 0:00

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