We present a computational strategy for reducing the sign problem in the evaluation of high dimensional integrals with nonpositive definite weights whose logarithms are analytic. The method involves stochastic sampling with a positive semidefinite weight that is adaptively and optimally determined during the course of a simulation. The optimal criterion, which follows from a variational principle for analytic actions $S(z)$, is a global stationary phase condition that the average gradient of the phase $\mathrm{I}\mathrm{m}S$ along the sampling path vanishes. Numerical results are presented from simulations of a model adapted from statistical field theories of classical fluids.

• Received 21 April 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.150201