"Fuzzy" tight-binding Monte Carlo method: A O(N) technique for calculating structural and electronic properties of materials.

We present a novel approach to computer simulations of the structural and electronic properties of materials that scales linearly with the number of electrons in the system. The approach is based on the following: (i) The introduction of a ``fuzzy'' Monte Carlo technique based on the approximate calculation of the total energy of the system. We show that a statistical error in the energy may be included in the thermal distribution via a new formulation of the Glauber dynamics of the Monte Carlo method. (ii) The calculation of the total energy via a recursion technique for a set of random initial states and a decomposition into individual atomic contributions. Applications to the simulation of liquid iron, silicon, and carbon are presented.