Global Monte Carlo algorithms for many-fermion systems

I discuss algorithms for simulating many-fermion systems via global updatings of auxiliary fields followed by an accept-reject stage which eliminates finite-step-size errors. When the system size is larger than the correlation length, these procedures should require computer time growing only slightly faster than linearly with the system volume V. A corrected Langevin scheme should asymptotically display a $V^{4/3}$ behavior, while the hybrid Monte Carlo scheme can behave as $V^{5/4}$. I present some tests of the latter algorithm on a simple model of interacting electrons on a two-dimensional lattice.