Unified approach to numerical transfer matrix methods for disordered systems : applications to mixed crystals and to elasticity percolation

It is shown that the Negative Eigenvalue Theorem and transfer matrix methods may be considered within a unified framework and generalized to compute projected densities of states or, more generally, any linear combination of matrix elements of the inverse of large symmetric random matrices. As examples of applications, extensive simulations for one- and two-mode behaviour in the Raman spectrum of one-dimensional mixed crystals and a finite-size scaling analysis of critical exponents for the central force percolation universality class are presented.