The discussion revolves around the role of Markov chains in the context of Metropolis Monte Carlo simulations applied to the Ising model. Participants explore the relationship between lattice site transitions, spin flips, and the probabilistic nature of these processes.
Participants generally agree on the concept that the probability of transitioning to a new lattice site depends only on the current state and not on the history of previous states. However, the initial confusion about the role of Markov chains suggests that some aspects of the discussion remain unresolved.
There may be limitations in the understanding of how Markov chains specifically apply to the simulation process, as well as potential ambiguities in the definitions of terms used in the discussion.
What do you mean by "probability distribution around the previous lattice site"?mathman said:The lattice site after a flip has a probability distribution around the previous lattice site.
Correct!LagrangeEuler said:Thanks. Let me see if I understood you well. So you are now at site ##i## and you fliping spin at that moment. Probablility that after fliping spin will stay in that position depends only of that current position of all spins at the lattice and not of the path that we did before it. Lattice does not remember which spins are moved earlier.