  We summarize the results recently reported in Ref.[1] [A. Deuzeman, M.P.
Lombardo, T. Nunes da Silva and E. Pallante,"The bulk transition of QCD with
twelve flavors and the role of improvement"] for the SU(3) gauge theory with
Nf=12 fundamental flavors, and we add some numerical evidence and theoretical
discussion. In particular, we study the nature of the bulk transition that
separates a chirally broken phase at strong coupling from a chirally restored
phase at weak coupling. When a non-improved action is used, a rapid crossover
is observed at small bare quark masses. Our results confirm a first order
nature for this transition, in agreement with previous results we obtained
using an improved action. As shown in Ref.[1], when improvement of the action
is used, the transition is preceded by a second rapid crossover at weaker
coupling and an exotic phase emerges, where chiral symmetry is not yet broken.
This can be explained [1] by the non hermiticity of the improved lattice
Transfer matrix, arising from the competition of nearest-neighbor and
non-nearest neighbor interactions, the latter introduced by improvement and
becoming increasingly relevant at strong coupling and coarse lattices. We
further comment on how improvement may generally affect any lattice system at
strong coupling, be it graphene or non abelian gauge theories inside or
slightly below the conformal window.
