Random updates or typewriter-to-copy?
Here it shouldn’t make any difference. Since we’re sampling an integral, there’s no concept of “time” – unlike the SIR model the Ising simulation is strictly at equilibrium, so the answers really should be the same. Equilibrium is tied up with detailed balance (the probability of visiting a microstate at any time is proportional to its Boltzmann factor. You may have seen this idea in Statistical Mechanics.
