Incompleteness of the Critical Exponent Description for Ferromagnetic Systems Containing Random Impurities

We consider the magnetic properties and spin correlation functions of a two-dimensional Ising model with random impurities near the critical temperature and find that the usual parametrization provided by the exponents $\gamma$, $\delta$, and $\eta$ and the correlation length $\xi$ for $T\gtrsim T_c$ does not describe our results. Experimental implications of this breakdown of the critical exponent forms are discussed.