Reentrant Ferromagnetic Ordering of the Random-Field Heisenberg Model in d>2 Dimensions: Fourier-Legendre Renormalization-Group Theory

The random-magnetic-field classical Heisenberg model is solved in spatial dimensions d>=2 using the recently developed Fourier-Legendre renormalization-group theory for $4\pi$ steradians continuously orientable spins, with renormalization-group flows of 12,500 variables. The random-magnetic-field Heisenberg model is exactly solved in 10 hierarchical models, for d=2,2.26,2.46,2.58,2.63,2.77,2.89,3. For non-zero random fields, ferromagnetic order is seen for d>2. This ordering shows, at d=3, reentrance as a function of temperature.Comment: 6 pages, 6 figures. arXiv admin note: text overlap with arXiv:2202.0604

On the magnetic fields, beaming fractions, and fastness parameters of pulsating ultraluminous x-ray sources

The discovery of pulsating ultraluminous X-ray sources (PULX) suggests that neutron stars are presumably common within the ultraluminous X-ray source (ULX) population though the majority of the population members currently lack pulsations. These systems are likely to host neutron stars accreting mass at super-Eddington (supercritical) rates from their massive companion in high-mass X-ray binaries. Taking into account the spherization of the accretion flow in the supercritical regime, the beaming of X-ray emission, and the reduction of the scattering cross section in a strong magnetic field, we infer the ranges for the neutron-star surface magnetic dipole field strengths, beaming fractions, and fastness parameters in the PULX M82 X-2, ULX NGC 5907, ULX NGC 7793 P13, NGC 300 ULX1, M51 ULX-7, NGC 1313 X-2, and Swift J0243.6+6124 from a set of conditions based on a variety of combinations of different spin and luminosity states. Using the observed spin-up rates under the critical luminosity condition, we estimate the surface-field strengths in the ∼1011–1013 G range for all PULX. In general, the results of our analysis under the subcritical luminosity condition indicate surface-field strengths in the ∼1011–1015 G range. We argue that PULX do not require magnetar-strength surface dipole fields if beaming is taken into account, yet the fields are strong enough for the neutron stars in ULX to magnetically channel the accretion flow in supercritical accretion disks