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Exact Solutions for One-Dimensional Systems with Short-Range Order

We consider one-dimensional disordered systems (e.g., harmonic, tight-binding, Ising,...) where the value of the random variable (e.g., mass, site energy, magnetic field,...) at a given site is correlated with the value at the previous site. For a certain class of transition probabilities we present exact solutions of the integrated density of states, inverse localization length, free energy,.... They involve infinite continued fractions with nonrandom coefficients.