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This review discusses a paradigm that has become of increasing importance inthe theory of quantum phase transitions; namely, the coupling of theorder-parameter fluctuations to other soft modes, and the resultingimpossibility of constructing a simple Landau-Ginzburg-Wilson theory in termsof the order parameter only. The soft modes in question are manifestations ofgeneric scale invariance, i.e., the appearance of long-range order in wholeregions in the phase diagram. The concept of generic scale invariance, and itsinfluence on critical behavior, is explained using various examples, bothclassical and quantum mechanical. The peculiarities of quantum phasetransitions are discussed, with emphasis on the fact that they are moresusceptible to the effects of generic scale invariance than their classicalcounterparts. Explicit examples include: the quantum ferromagnetic transitionin metals, with or without quenched disorder; the metal-superconductortransition at zero temperature; and the quantum antiferromagnetic transition.Analogies with classical phase transitions in liquid crystals and classicalfluids are pointed out, and a unifying conceptual framework is developed forall transitions that are influenced by generic scale invariance.Comment: 55pp, 25 eps figs; final version, to appear in Rev Mod Phy

How generic scale invariance influences quantum and classical phase transitions