2001/06/14 by D. Belitz, T. R. Kirkpatrick
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.str-el
published as J. Low Temp. Phys. 126, 1107 (2002) · 15 pp., LaTeX, 1 eps fig, requires style file jltp.cls (included)
arxiv created 2001/06/14 · arxiv updated 2009/11/30
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.