We study the behavior of the dual quark condensate σ<inf>1</inf> in the Nambu-Jona-Lasinio (NJL) model and its nonlocal variant. In quantum chromodynamics σ<inf>1</inf> can be related to the breaking of the center symmetry and is therefore an (approximate) order parameter of confinement. The deconfinement transition is then signaled by a strong rise of σ<inf>1</inf> as a function of temperature. However, a similar behavior is also seen in the NJL model, which is known to have no confinement. Indeed, it was shown that in this model the rise of σ<inf>1</inf> is triggered by the chiral phase transition. In order to shed more light on this issue, we calculate σ<inf>1</inf> for several variants of the NJL model, some of which have been suggested to be confining. Switching between "confining" and "non-confining" models and parametrizations we find no qualitative difference in the behavior of σ<inf>1</inf>, namely, it always rises in the region of the chiral phase transition. We conclude that without having established a relation to the center symmetry in a given model, σ<inf>1</inf> should not blindly be regarded as an order parameter of confinement.
Marquez, F., Ahmad, A., Buballa, M., & Raya, A. (2015). The dual quark condensate in local and nonlocal NJL models: An order parameter for deconfinement? Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 747, 529–535. https://doi.org/10.1016/j.physletb.2015.06.031