SciPost Phys. 5, 050 (2018) ·
published 22 November 2018

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We study complex CFTs describing fixed points of the twodimensional
$Q$state Potts model with $Q>4$. Their existence is closely related to the
weak firstorder 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 twoloop
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 5state dilute Potts model with complexified temperature and vacancy
fugacity.