Microscopic study of 3D Potts phase transition via Fuzzy Sphere Regularization

TL;DR

This study investigates the phase transition in a 3D quantum Potts model with Q=3 using fuzzy sphere regularization, revealing approximate conformal symmetry and pseudo-critical behavior indicative of a complex fixed point.

Contribution

It introduces a microscopic model for the 3D quantum Potts transition and uncovers evidence of conformal symmetry and pseudo-criticality through finite-size analysis.

Findings

Energy spectrum shows approximate conformal symmetry at transition.

Subleading operator dimension drifts around critical value ~3.

Transition appears discontinuous with pseudo-critical behavior.

Abstract

The Potts model describes interacting spins with $Q$ different components, which is a direct generalization of the Ising model ($Q=2$). Compared to the existing exact solutions in 2D, the phase transitions and critical phenomena in the 3D Potts model have been less explored. Here, we systematically investigate a quantum $(2+1)$-D Potts model with $Q=3$ using a fuzzy sphere regularization scheme. We first construct a microscopic model capable of achieving a magnetic phase transition that separates a spin $S_3$ permutationally symmetric paramagnet and a spontaneous symmetry-breaking ferromagnet. Importantly, the energy spectrum at the phase transition point exhibits an approximately conformal symmetry, implying that an underlying conformal field theory may govern this transition. Moreover, when tuning along the phase transition line in the mapped phase diagram, we find that the dimension of the subleading $S_3$ singlet operator flows and drifts around the critical value $\sim 3$, which is believed to be crucial for understanding this phase transition, although determining its precise value remains challenging due to the limitations of our finite-size calculations. These findings suggest a discontinuous transition in the 3D 3-state Potts model, characterized by pseudo-critical behavior, which we argue results from a nearby multicritical or complex fixed point.