Why Quantum Phase Transitions Are Interesting

This paper discusses why the usual notion that quantum phase transitions can be mapped onto classical phase transitions in a higher dimension, and that this makes the former uninteresting from a fundamental theoretical point of view, is in general misleading. It is shown that quantum phase transitions are often qualitatively different from their classical counterparts due to (1) long ranged effective interactions that are induced by soft modes, and (2) in the presence of quenched disorder, an extreme anisotropy of space time. These points are illustrated using various magnetic phase transitions as examples.