Global Stationary Phase and the Sign Problem

Abstract

We present a computational strategy for reducing the sign problem in the evaluation of high dimensional integrals with non-positive definite weights. 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 Im(S) along the sampling path vanishes. Numerical results are presented from simulations of a model adapted from statistical field theories of classical fluids.