Continuous Quantum Phase Transitions
  A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. We show that considerable insight is gained by considering the path integral description of the quantum statistical mechanics of such systems, which takes the form of the {\em classical} statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite temperature behavior, which turns out to be described by the theory of finite size scaling. It also leads naturally to the notion of a temperature-dependent dephasing length that governs the crossover between quantum and classical fluctuations. We illustrate these ideas using Josephson junction arrays and with a set of recent experiments on phase transitions in systems exhibiting the quantum Hall effect. 
S. L. Sondhi, S. M. Girvin, J. P. Carini and D. Shahar