  Excitations of disordered systems such as glasses are of fundamental and
practical interest but computationally very expensive to solve. Here we
introduce a technique for modeling these excitations in an infinite disordered
medium with a reasonable computational cost. The technique relies on a discrete
atomic model to simulate the low-energy behavior of an atomic lattice with
molecular impurities. The interaction between different atoms is approximated
using a spring like interaction based on the Lennard Jones potential but can be
easily adapted to other potentials. The technique allows to solve a
statistically representative number of samples with a minimum of computational
expense, and uses a Monte-Carlo approach to achieve a state corresponding to
any given temperature. This technique has already been applied successfully to
a problem with interest in condensed matter physics: the solid solution of
N$_2$ in Ar.
