Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at $Q>4$

TL;DR

This paper investigates complex conformal field theories related to the two-dimensional Potts model with more than four states, revealing their role in weak first-order transitions and walking RG behavior, and providing predictions for Monte Carlo detection.

Contribution

It introduces a detailed analysis of complex CFTs in the Q>4 Potts model, connecting them to walking RG flows and providing conformal data and predictions for simulations.

Findings

Identification of complex CFTs with specific properties

Prediction of $S_5$-symmetric complex CFTs with complex central charges

Connection between complex CFTs and observable walking RG behavior

Abstract

We study complex CFTs describing fixed points of the two-dimensional $Q$-state Potts model with $Q>4$. Their existence is closely related to the weak first-order phase transition and walking RG behavior present in the real Potts model at $Q>4$. The Potts model, apart from its own significance, serves as an ideal playground for testing this very general relation. Cluster formulation provides nonperturbative definition for a continuous range of parameter $Q$, while Coulomb gas description and connection to minimal models provide some conformal data of the complex CFTs. We use one and two-loop conformal perturbation theory around complex CFTs to compute various properties of the real walking RG flow. These properties, such as drifting scaling dimensions, appear to be common features of the QFTs with walking RG flows, and can serve as a smoking gun for detecting walking in Monte Carlo simulations. The complex CFTs discussed in this work are perfectly well defined, and can in principle be seen in Monte Carlo simulations with complexified coupling constants. In particular, we predict a pair of $S_5$-symmetric complex CFTs with central charges $c\approx 1.138 \pm 0.021 i$ describing the fixed points of a 5-state dilute Potts model with complexified temperature and vacancy fugacity.