Recent theoretical and experimental studies of superfluid ${}^3\text{H}\text{e}$ in aerogels with a global anisotropy created, e.g., by an external stress have definitely shown that the $A$-like phase with an equal-spin pairing in such aerogel samples is in the Anderson-Brinkman-Morel (ABM) (or axial) pairing state. In this paper, the $A$-like phase of superfluid ${}^3\text{H}\text{e}$ in globally isotropic aerogel is studied in detail by assuming a weakly disordered system in which singular topological defects are absent. Through calculation of the free energy, a disordered ABM state is found to be the best candidate of the pairing state of the globally isotropic $A$-like phase. Further, it is found through a one-loop renormalization-group calculation that the coreless continuous vortices (or vortex-Skyrmions) are irrelevant to the long-distance behavior of disorder-induced textures, and that the superfluidity is maintained in spite of lack of the conventional superfluid long-range order. Therefore, the globally isotropic $A$-like phase at weak disorder is, like in the case with a globally stretched anisotropy, a glass phase with the ABM pairing and shows superfluidity.

• Received 14 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.064527