The manuscript tilted “Rigidity transitions in anisotropic networks happen in multiple steps” authored by William Y. Wang et. al discussed about the difference of rigidity transition between isotropic and anisotropic bonds percolated clusters. In the process they are also proposing universality scaling function for rigidity transition as a multicritical point. The manuscript is well written and may contributes to knowledge of cell cytoskeleton rigidity understanding as well. What I found strange is that although it is submitted as an article, the format the manuscript is more letter like. I would suggest the authors to make the manuscript more in an article format for the ease of readers.
The simulation details most of the part are in the appendix, which mostly should be part of the main manuscript.
In the case of anisotropic rigidity the authors have shown the p_c changes. I agree the power law can change why should p_c change as you will have to remove the same average number of bonds?
Assuming that effective medium theory is independently applied along different axis with the anisotopic parameter it should prediction should be correct, if not why it is not giving the right results? (or I have completely misunderstood this point)
The term floppy is generally used when the particles can diffuse and rearrange without breaking the bonds, which is quite different from what the authors have in mind. See for example: Phys. Rev. E 75, 011406 (2007) or Eur. Phys. J. E 27, 297–308 (2008).