The bulk transition of QCD with twelve flavors and the role of improvement

We study the SU(3) gauge theory with Nf=12 flavors in the fundamental representation by use of lattice simulations with staggered fermions. With a non-improved action we observe a chiral zero-temperature (bulk) transition separating a region at weak coupling, where chiral symmetry is realized, from a region at strong coupling where chiral symmetry is broken. With improved actions, a more complicated pattern emerges, and in particular two first order transitions in the chiral limit appear. We observe that at sufficiently strong coupling the next-to-nearest neighbor terms of the improved lattice action are no longer irrelevant and can indeed modify the pattern observed without improvement. Baryon number conservation can be realized in an unusual way, allowing for an otherwise prohibited oscillating term in the pseudoscalar channel. We discuss the phenomenon by means of explicit examples borrowed from statistical mechanics. Finally, these observations can also be useful when simulating other strongly coupled systems on the lattice, such as graphene.