Quantum Phase Transitions

Abstract Thermal fluctuations induced by increasing temperature can change the state of matter, for example, when water boils to steam. It also is possible to change the state of matter at absolute zero temperature by quantum fluctuations demanded by Heisenberg's uncertainty principle. In this case, the quantumphase transition from one state to another is provided by adjusting a tuning parameter other than temperature. A few characteristic examples of quantumphase transitions are reviewed, and their consequences for finite temperature experiments are discussed.