We compute the Polyakov loop potential in Yang-Mills theory from the fully dressed primitively divergent correlation functions only. This is done in a variety of functional approaches ranging from functional renormalization group equations over Dyson-Schwinger equations to two-particle irreducible functionals. We present a confinement criterion that links the infrared behavior of propagators and vertices to the Polyakov loop expectation value. The present work extends the works of [J. Braun et al., Phys. Lett. B 684, 262 (2010); F. Marhauser and J. M. Pawlowski, arXiv:0812.1144; J. Braun et al., Eur. Phys. J. C 70, 689 (2010)] to general functional methods and sharpens the confinement criterion presented there. The computations are based on the thermal correlation functions in the Landau gauge calculated in [L. Fister and J. M. Pawlowski, arXiv:1112.5440; L. Fister and J. M. Pawlowski, arXiv:1112.5429; L. Fister, Ph.D. thesis, Heidelberg University, 2012].

• Received 5 March 2013

DOI:https://doi.org/10.1103/PhysRevD.88.045010