On simulating complex actions

Abstract We describe and compare various methods to numerically simulate measures that are non-positive definite. We argue that variations of importance sampling will fail for large enough volume but some type of Riemann integration scheme might work. Using exact results for the three-dimensional Ising model, we show that to get anything distinguishable from noise, the phase of the measure must be known extremely precisely. We suggest that a recent method to compute the density of states may be the best method to use.