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 a renormalization group procedure. Somewhat surprisingly, the critical behavior is completely independent of $q$. For the $q>\mathrm{}4\mathrm{}$ clock model, we suggest the existence of a novel multicritical point at intermediate randomness. We also consider the $T=0\mathrm{}$ transition from a paramagnet to a spin glass in an infinite-range model, and find $q$ independent exponents.