Degenerate and critical Bloch branes

In the last few years a number of works reported the appearance of thick branes with internal structure, induced by the parameter which controls the interaction between two scalar fields coupled to gravity in (4,1) dimensions in warped space-time with one extra dimension. Here we show that one can implement the control over the brane thickness without needing to change the potential parameter. On the contrary, this is going to be done by means of the variation of a parameter associated to the domain wall degeneracy. We also report the existence of novel and qualitatively different solutions for a critical value of the degeneracy parameter, which could be called critical Bloch branes.