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

Phase transitions induced by microscopic disorder: a study based on the order parameter expansion