  Numerical simulations based on electronic structure calculations are finding
ever growing applications in many areas of physics. A major limiting factor is
however the cubic scaling of the algorithms used. Building on previous work [F.
R. Krajewski and M. Parrinello, Phys.Rev. B71, 233105 (2005)] we introduce a
novel statistical method for evaluating the inter-atomic forces which scales
linearly with system size and is applicable also to metals. The method is based
on exact decomposition of the fermionic determinant and on a mapping onto a
field theoretical expression. We solve exactly the problem of sampling the
Boltzmann distribution with noisy forces. This novel approach can be used in
such diverse fields as quantum chromodynamics, quantum Monte Carlo or colloidal
physics.
