  We present a practical solution to the "sign problem" in the auxiliary field
Monte Carlo approach to the nuclear shell model. The method is based on
extrapolation from a continuous family of problem-free Hamiltonians. To
demonstrate the resultant ability to treat large shell-model problems, we
present results for 54Fe in the full fp-shell basis using the Brown-Richter
interaction. We find the Gamow-Teller beta^+ strength to be quenched by 58%
relative to the single-particle estimate, in better agreement with experiment
than previous estimates based on truncated bases.
