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Abstract: Recent theoretical and experimental studies of superfluid $^3$He in aerogelswith a global anisotropy, e.g., due to an external stress, have definitelyshown that the A-like phase with an equal spin pairing ESP in such aerogelsamples is in the ABM or, axial pairing state. In this paper, the A-likephase of superfluid $^3$He in globally {\it isotropic} aerogel is studied indetails by assuming a weakly disordered system in which singular topologicaldefects are absent. Through calculation of the free energy, a disordered ABMstate is found to be the best candidate of the pairing state of the globallyisotropic A-like phase. Further, it is found through a one-loop renormalizationgroup calculation that the coreless continuous vortices or, vortex-skyrmionsare irrelevant to the long-distance behavior of the disorder-induced textures,and that the superfluidity is maintained in spite of lack of the conventionaloff-diagonal long range order. Therefore, the globally isotropic A-like phaseat weak disorder is, like in the case with a global stretched anisotropy, asuperfluid glass with the ABM pairing.

Autor: Ryusuke Ikeda, Kazushi Aoyama


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