Why do local updates (i.e. local spin flips) near the phase transition in MC algorithm for classical 2D Ising model are said to be not "effective" and lead to incorrect critical indices? I understand that it is somehow connected with infinite correlation length, but how exactly? Does it mean that near phase transition it takes infinite time for algorithm to achieve equilibrium distribution?

  • $\begingroup$ Can you provide a reference for what you're referring to? $\endgroup$
    – lemon
    May 29, 2017 at 10:14
  • $\begingroup$ Here, for instance, physics.buffalo.edu/phy411-506/topic2/topic2-lec4.pdf Probably I don't understand the particular sentence "The Metropolis Monte Carlo method generates successive configurations of spins, but this does not represent the real time evolution of a system of spins." So why do I need to consider cluster algorithms? $\endgroup$
    – Whys
    May 29, 2017 at 10:22
  • $\begingroup$ It is explained in the slides you cited in the previous comment that the critical slowing down is due to the divergence of the relaxation time when the critical temperature is approached. What is exactly that doesn't satisfy you in this explanation? $\endgroup$
    – valerio
    May 29, 2017 at 11:07
  • $\begingroup$ I don't understand why cluster algorithms (that flip group of spin in one Monte-Carlo step) improve convergence of the algorithm? $\endgroup$
    – Whys
    May 29, 2017 at 11:32
  • $\begingroup$ It seems that the link to the lecture that you posted no longer takes one to the lecture notes... $\endgroup$
    – Floris
    Oct 10, 2017 at 14:16


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