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 Dec 11 awarded Popular Question Jun 25 awarded Scholar Jun 25 accepted What is probability to find electron at certain distance from nucleus Jun 24 asked What is probability to find electron at certain distance from nucleus Jun 16 revised Are higher order mixed partial derivatives of wave function with different ordination equal? Corrected title because question is not necessarily connected with commutator Jun 16 asked Are higher order mixed partial derivatives of wave function with different ordination equal? Aug 16 comment Importance of Kohn anomaly? Sorry, I can't see what's wrong with this? It's very specific and I believe person with experience should describe it in a few words. Besides, I can't find answer on wiki, nor elsewhere. If someone could point out where on wiki answer is, i would be grateful and apologize for recklessness. Aug 16 awarded Editor Aug 16 revised Importance of Kohn anomaly? edited title Aug 16 asked Importance of Kohn anomaly? Mar 12 comment Efficiency of Metropolis algorithm It seems that main problem is with low acceptance ratio which grows with temperature, so is small on low temperatures. Can I conclude that short answer on both of my qeustions could be: Metropolis algorithm is not efficient at low tmperatures because of low accceptance ratio on that temperatures? And acceptance ratio is low because of low/narrow accptance probability (as thoroughly explained in answers). Mar 12 comment Efficiency of Metropolis algorithm (continued).. The equilibrium state will have most spins pointing down. Nevertheless, if the magnetic field is small and the temperature is low enough, equilibrium will take a very long time to occur. What we need is a more efficient way of sampling configurations if the acceptance probability is low." (end of quote). Mar 12 comment Efficiency of Metropolis algorithm @genneth: Thanks for answers. But in literature I exactly found that algorithm is not efficient at low temperatures, not near critical temperature (although same thing in 1D). Gould and Tobochnik maybe gives an explanation in their "Computer simulation methods" on page 652.: "Monte Carlo simulations become very inefficient at low temperatures because almost all trial configurations will be rejected. For example consider an Ising model (not only 1D) for which all spins are up, but a small magnetic field is applied in the negative direction... Mar 8 comment Efficiency of Metropolis algorithm I deleted my comment because I just understand things for which I asked clarification. Now I need confirmation please: Suppose 1) $T\neq 0$, 2) correlation length is larger than the sample (and model quickly anneal to ferromagnetic state), 3) external magnetic field $H =0$. Does that mean that average magnetisation of the sample in equilibrium doesn't have to be 0? I am asking that because in 1d simulation model which I investigate I got average magnetisation to not be zero for all $T\leq0.2$ . Thanks Feb 26 awarded Supporter Feb 25 awarded Quorum Feb 24 awarded Student Feb 24 asked Efficiency of Metropolis algorithm