Exact solution of the impure one-dimensional n-vector model with bilinear and biquadratic exchange interactions

We demonstrate explicitly that the impure one-dimensional n-vector model with bilinear and biquadratic exchange interactions can be solved exactly. Results are provided for the free energy, equal-time spin-spin correlation functions and the initial susceptibility of the corresponding bond and site model in the annealed and quenched limit. A numerical analysis of the thermodynamic response functions in the n = 3 case is performed, and therein some interesting consequences of the simultaneous influence of the biquadratic interactions and impurities are established. The presence of the biquadratic interaction is interpreted as an effect of the lattice compressibility.