  In this work, we employ renormalization group methods to study the general
behavior of field theories possessing anisotropic scaling in the spacetime
variables. The Lorentz breaking symmetry that accompanies these models are
either soft, if no higher spatial derivative is present, or it may have a more
complex structure if higher spatial derivatives are also included. Both
situations are discussed in models with only scalar fields and also in models
with fermions as a Yukawa like model.
