Critical Properties of Random Quantum Potts and Clock Models

TL;DR

This paper investigates zero temperature phase transitions in random quantum Potts and clock models, revealing q-independent critical properties and proposing a new multicritical point for clock models with q>4.

Contribution

It provides exact RG analysis of ferromagnetic quantum Potts and clock models, uncovering q-independent critical behavior and suggesting a novel multicritical point at intermediate randomness.

Findings

Second order transition with q-independent critical exponents

Existence of a multicritical point for q>4 clock models

Critical behavior in infinite range models with q-independent exponents

Abstract

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.