### Abstract

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. Considerable insight is gained by considering the path-integral description of the quantum statistical mechanics of such systems, which takes the form of the 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. Using these ideas, a scaling analysis of experiments on Josephson-junction arrays and quantum-Hall-effect systems is presented.

Original language | English (US) |
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Pages (from-to) | 315-333 |

Number of pages | 19 |

Journal | Reviews of Modern Physics |

Volume | 69 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1997 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*Reviews of Modern Physics*,

*69*(1), 315-333. https://doi.org/10.1103/revmodphys.69.315