Stella, A. L.Swift, Michael R.Amar, Jacques G.Einstein, Theodore L.Cole, M. W.Banavar, Jayanth .The effect of inhomogeneous couplings of the scaling behavior in critical phenomena is considered using renormalization group analysis, Monte Carlo simulations, and other numerical tests. Novel scaling relationships result from nonuniform perturbations of a uniform fixed point at criticality. An effective dimension entering scaling equalities is elucidated. Nonuniversal behavior is found in fully connected systems with exchange couplings arrayed in a hierarchical manner.Article