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 $2 \leq q < \infty$). 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.