Reviews of Modern Physics, Vol. 77, No. 2, pp. 579-632, April 2005

## How generic scale invariance influences quantum and classical phase transitions

### by D. Belitz, T.R. Kirkpatrick, and Thomas Vojta

This review discusses a paradigm that has become of increasing importance in
the theory of quantum phase transitions, namely, the coupling of the
order-parameter fluctuations to other soft modes and the resulting
impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms
of the order parameter only. The soft modes in question are manifestations of
generic scale invariance, i.e., the appearance of long-range order in whole
regions in the phase diagram. The concept of generic scale invariance and its
influence on critical behavior is explained using various examples, both
classical and quantum mechanical. The peculiarities of quantum phase
transitions are discussed, with emphasis on the fact that they are more
susceptible to the effects of generic scale invariance than their classical
counterparts. Explicit examples include the quantum ferromagnetic transition in
metals, with or without quenched disorder; the metal-superconductor transition
at zero temperature; and the quantum antiferromagnetic transition. Analogies
with classical phase transitions in liquid crystals and classical fluids are
pointed out, and a unifying conceptual framework is developed for all
transitions that are influenced by generic scale invariance.
Complete paper (e-print version)