Exploring the phase structure of 12-flavor $SU(3)$

We are studying the $SU(3)$ gauge theory with 12 staggered fermions, searching for the endpoint of the line of first-order phase transitions in the mass–beta plane. This endpoint plays an important role in our understanding of the phase diagram of this model. Having found this endpoint with high statistics on a small lattice using unimproved staggered fermions, we are working to find it on larger lattices and with improved actions. For an action improved with nHYP-smeared staggered fermions, we discuss the effect of slowly turning off the improvement on the broken shift symmetry phase.