Based on the order parameter expansion, we present an approximate method
which allows us to reduce large systems of coupled differential equations with
diverse parameters to three equations: one for the global, mean field, variable
and two which describe the fluctuations around this mean value. With this tool
we analyze phase-transitions induced by microscopic disorder in three
prototypical models of phase-transitions which have been studied previously in
the presence of thermal noise. We study how macroscopic order is induced or
destroyed by time independent local disorder and analyze the limits of the
approximation by comparing the results with the numerical solutions of the
self-consistency equation which arises from the property of self-averaging.
Finally, we carry on a finite-size analysis of the numerical results and
calculate the corresponding critical exponents