Phase transitions and singularities in random quantum systems

Random quantum systems that exhibit unusual behavior associated with “infinite randomness” fixed points are discussed, focusing on the random quantum Ising model. This system undergoes a transition at zero temperature from a phase with infinite susceptibility and continuously variable exponents to a ferromagnetic phase via a quantum critical point characterized by “tunneling scaling” with energy Ω and length scales, L, related by 1n Ω Lψ. Exact results in one dimension and a scaling picture in higher dimensions are derived from a simple renormalization group. Other random quantum critical points and quantum disordered phases that can exhibit similar features are discussed briefly.