Critical properties of random quantum Potts and clock models.

We study zero temperature phase transitions in two classes of random quantum systems -the q-state quantum Potts and clock models. For models with purely ferromagnetic interactions in one dimension, we show that for strong randomness there is a second order transition with critical properties that can be determined exactly by use of an RG procedure. Somewhat surprisingly, the critical behaviour is completely independent of q (for 2 ≤ q < ∞). For the q > 4 clock model, we suggest the existence of a novel multicritical point at intermediate randomness. We also consider the T = 0 transition from a paramagnet to a spin glass in an infinite range model. Assuming that the transition is second order, we solve for the critical behaviour and find q independent exponents. PACS numbers:75.10.Nr, 05.50.+q, 75.10.Jm Typeset using REVTEX