  We unveil the general features of the phase diagram for any gauge theory with
fermions transforming according to distinct representations of the underlying
gauge group, at the four-loop order. We classify and analyze the zeros of the
perturbative beta function and discover the existence of a rich phase diagram.
The anomalous dimension of the fermion masses, at the infrared stable fixed
point, are presented. We show that the infrared fixed point, and associated
anomalous dimension, are well described by the all-orders beta function for any
theory. We also argue the possible existence, to all orders, of a nontrivial
ultraviolet fixed point for gauge theories at large number of flavors.
