  Accreting highly magnetized pulsars in binary systems are among the brightest
X-ray emitters in our Galaxy. Although a number of high statistical quality
broad-band (0.1-100 keV) X-ray observations are available, the spectral energy
distribution of these sources is usually investigated by adopting pure
phenomenological models, rather than models linked to the physics of accretion.
In this paper, a detailed spectral study of the X-ray emission recorded from
the high-mass X-ray binary pulsars Cen X-3, 4U 0115+63, and Her X-1 is carried
out by using BeppoSAX and joined Suzaku+NuStar data, together with an advanced
version of the compmag model. The latter provides a physical description of the
high energy emission from accreting pulsars, including the thermal and bulk
Comptonization of cyclotron and bremsstrahlung seed photons along the neutron
star accretion column. The compmag model is based on an iterative method for
solving second-order partial differential equations, whose convergence
algorithm has been improved and consolidated during the preparation of this
paper. Our analysis shows that the broad-band X-ray continuum of all considered
sources can be self-consistently described by the compmag model. The cyclotron
absorption features, not included in the model, can be accounted for by using
Gaussian components. From the fits of the compmag model to the data we inferred
the physical properties of the accretion columns in all sources, finding values
reasonably close to those theoretically expected according to our current
understanding of accretion in highly magnetized neutron stars. The updated
version of the compmag model has been tailored to the physical processes that
are known to occur in the columns of highly magnetized accreting neutron stars
and it can thus provide a better understanding of the high energy radiation
from these sources.
