Quantum phase transitions in antiferromagnets and super fluids

We present a general introduction to the non-zero temperature dynamic and t ransport properties of low-dimensional systems near a quantum phase transit ion. Basic results are reviewed in the context of experiments on the spin-l adder compounds, insulating two-dimensional antiferromagnets, and double-la yer quantum Hall systems. Recent large N computations on an extended t-J mo del (Phys. Rev. Lett. 83 (1999) 3916) motivate a global scenario of the qua ntum phases and transitions in the high-temperature superconductors, and co nnections are made to numerous experiments. (C) 2000 Elsevier Science B.V. All rights reserved.