Understanding Markov Chains in Metropolis Monte Carlo Ising Simulation

[LagrangeEuler]

I do not understand where are Markov chains in Monte Carlo Ising simulation. Going randomly from lattice site to lattice site one flip one spin calculates energy and goes ahaid. But where are Markov chain there? Could you please explain me this. Thanks a lot.

 

[mathman]

The lattice site after a flip has a probability distribution around the previous lattice site.

 

[LagrangeEuler]

The lattice site after a flip has a probability distribution around the previous lattice site.

What do you mean by "probability distribution around the previous lattice site"?

 

[mathman]

The choice of the next lattice site is random. However it is defined in terms of a displacement from the current lattice site.

 

[LagrangeEuler]

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.

 

[mathman]

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.

Correct!