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

We study complex CFTs describing fixed points of the two-dimensional$Q$-state Potts model with $Q>4$. Their existence is closely related to theweak first-order phase transition and walking RG behavior present in the realPotts model at $Q>4$. The Potts model, apart from its own significance, se...

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Bibliographic Details
Published inSciPost physics Vol. 5; no. 5; p. 050
Main Authors Gorbenko, Victor, Rychkov, Slava, Zan, Bernardo
Format Journal Article
LanguageEnglish
Published SciPost Foundation 01.11.2018
SciPost
Subjects
General Physics
High Energy Physics - Lattice
High Energy Physics - Phenomenology
High Energy Physics - Theory
Physics
model: minimal
cluster
nonperturbative
dimension: 2
critical phenomena
numerical calculations: Monte Carlo
Potts model
field theory
field theory: conformal
central charge
perturbation theory
fixed point
gas: Coulomb
temperature
renormalization group: flow
scaling: dimension
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Summary:We study complex CFTs describing fixed points of the two-dimensional$Q$-state Potts model with $Q>4$. Their existence is closely related to theweak first-order phase transition and walking RG behavior present in the realPotts model at $Q>4$. The Potts model, apart from its own significance, servesas an ideal playground for testing this very general relation. Clusterformulation provides nonperturbative definition for a continuous range ofparameter $Q$, while Coulomb gas description and connection to minimal modelsprovide some conformal data of the complex CFTs. We use one and two-loopconformal perturbation theory around complex CFTs to compute various propertiesof the real walking RG flow. These properties, such as drifting scalingdimensions, appear to be common features of the QFTs with walking RG flows, andcan serve as a smoking gun for detecting walking in Monte Carlo simulations.The complex CFTs discussed in this work are perfectly well defined, and canin principle be seen in Monte Carlo simulations with complexified couplingconstants. In particular, we predict a pair of $S_5$-symmetric complex CFTswith central charges $c\approx 1.138 \pm 0.021 i$ describing the fixed pointsof a 5-state dilute Potts model with complexified temperature and vacancyfugacity.
ISSN:2542-4653
2542-4653
DOI:10.21468/SciPostPhys.5.5.050