Recent observations of surface emission from isolated neutron stars (NSs) provide unique challenges to theoretical modeling of thermal radiative processes. We construct models of thermal emission from strongly magnetized NSs in which the outermost layer of the NS is in a condensed liquid or solid form, or is an ionized H or He atmosphere.

We calculate the emission properties (spectrum and polarization) of NSs with condensed Fe and H surfaces using a generalized form of Kirchhoff's Law, in the regimes where condensation may be possible. For smooth condensed surfaces, the overall emission is reduced from blackbody by less than a factor of two. The spectrum exhibits modest deviation from blackbody across a wide energy range, and shows mild absorption features associated with the electron plasma and ion cyclotron frequencies in the condensed matter. The roughness of the solid Fe condensate decreases the reflectivity of the surface, making the emission spectrum even closer to blackbody.

We provide an accurate treatment of vacuum polarization effects in magnetized NS atmosphere models. We treat the conversion of photon modes (due to ``vacuum resonance'' between plasma and vacuum polarizations), employing both the modal radiative transfer equations (coupled with an accurate mode conversion probability at the vacuum resonance) and the full radiative transfer equations for the photon Stokes parameters. We are able to quantitatively calculate the atmosphere structure, emission spectra, beam patterns, and polarizations for the range of magnetic field strengths $B=1012-1015$ G. In agreement with previous studies, we find that for NSs with magnetic field strengths $B/2\backslash gaBl\simeq 7\times 1013$ G, vacuum polarization reduces the widths of spectral features and softens the hard tail of magnetized atmosphere models. For $B\backslash laBl/2$, vacuum polarization does not change the emission spectra, but can affect the polarization signals.

We investigate the propagation of photon polarization in NS magnetospheres, and show that vacuum polarization induces a unique energy-dependent linear polarization signature, and can generate circular polarization in the magnetospheres of rapidly rotating NSs. We discuss the implications of our results for observations of thermally emitting isolated NSs and magnetars, and the prospects for future spectral and polarization studies.