State transitions triggered by inverse magnetic field: probably applied in high-mass X-ray binaries?

Previous works suggested that the state transitions in an X-ray binary can be triggered by accreting inverse magnetic field from its companion star. A key point of this mechanism is the accretion and magnification of large-scale magnetic fields from outer boundary of a thin disk. However, how such a process can be realized is still an open question. In this work, we check this issue in a realistic X-ray binary system. According to our calculations, a quite strong initial magnetic field $B\sim 10^2-10^3$ G is required in order to assure that the large-scale magnetic field can be effectively dragged inward and magnified with the accretion of gas. Thus, such a picture probably can be present in high-mass X-ray binaries possessing strong stellar magnetic field, e.g., Cyg X-1.