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Critical Slowing Down

A problem with Monte Carlo (MC) simulation is that the error decreases only as , so need to do 100 times more work to get one more significant figure accuracy. Unfortunately, things are even worse. Error is only for N independent measurements. But MC configurations are usually correlated --- depends on .

Measure the autocorrelation function (similar to correlation function except in computer time, not real space) for an operator (measurement) A:

is the (exponential) autocorrelation time, and is equivalent to the which measures equilibration time of the Markov process. Need to thermalize for time .

Paul Coddington, Northeast Parallel Architectures Center at Syracuse University,