A general question to the Monte Carlo experts. When I use Wolff algorithm for global updates, say for Ising 2d, I always flip at least one spin (the initial random spin in the cluster). So, near the critical temperature when coming from below - where this should converge much faster than Metropolis' single flip - to a finite magnetization, we will always have strong osicillations because in each iteration we flip at least one spin with probability one. So we can't get rid of oscillations in this procedure, although they get weaker with higher temperature, where we can't flip more than one spin because of the low acceptance probability. Indeed in my matlab code I always see oscillations. Also near the critical temperature. What am I missing?

  • $\begingroup$ You mean you observe "oscillations" in the magnetisation as a function of the time step? Are these oscillations periodic or just fluctuations? $\endgroup$ – lr1985 Jan 8 '19 at 7:46
  • $\begingroup$ Hi, Well this is essentially , jumping between the two ground states of the ising model. if for example i take a lattice of 10X10 , after few time steps i can go from M=100 to M=-100. i need to stress that it happens even though i have a small external MF. so the flip is accepted if my random number is less than: 1-exp(-2*beta(J+H*initial_spin)) . and of course the spin is parallel to the initial random one $\endgroup$ – Ori Grossman Jan 8 '19 at 9:54
  • $\begingroup$ The point is , since i always flip at least one, even if i reach quickly to the minima of the system- the single flips , gradually pull me out of there $\endgroup$ – Ori Grossman Jan 8 '19 at 10:11
  • $\begingroup$ Could you include a graphic of the oscillations you are getting and what you expect you should get? $\endgroup$ – Kyle Kanos Jan 8 '19 at 11:07
  • $\begingroup$ @OriGrossman Isn't that the point of cluster updates: They allow you to go between the two symmetry broken clusters in few update steps, whereas Metropolis would never get there? $\endgroup$ – Norbert Schuch Jan 8 '19 at 11:13