A common example to introduce Monte-Carlo methods in statistical mechanics is to work out the properties of the 2D square lattice Ising model and compare the obtained results with Onsager's exact solution. One generally works with single "spin flip" dynamics (SFD) to update the spin configurations in the 2D Ising model. However, other types of updates can be used as long as they satisfy ergodicity and detailed balance. Now my question is the following:
Since different types of updates lead to the same equilibrium state, can we ascribe any physical significance to a specific type of update ?
I've seen comments like: this model is glassy under SFD.
But does that tell us anything about the equilibrium properties ?
Finally, some non-local algorithm (so-called worms algorithms) can be used to equilibrate constrained models (such as ice type models). Do these "worm" carry any physical significance for the real physical system ?
Yet another example (again from spin systems) are the so-called facilitated spin models, where the low energy excitations are some non-trivial plaquette moves. I believe that these models are glassy under SFP dynamics.