Loop expansion around the Bethe solution for the random magnetic field Ising ferromagnets at zero temperature
We apply to the random-field Ising model at zero temperature (T = 0) the perturbative loop expansion around the Bethe solution. A comparison with the standard ε expansion is made, highlighting the key differences that make the expansion around the Bethe solution much more appropriate to correctly describe strongly disordered systems, especially those controlled by a T = 0 renormalization group (RG) fixed point. The latter loop expansion produces an effective theory with cubic vertices.