  The influence of a constant uniform magnetic field on the thermodynamic
properties of a partially ionized hydrogen plasma is studied. Using the method
of Green' s function various interaction contributions to the thermodynamic
functions are calculated. The equation of state of a quantum magnetized plasma
is presented within the framework of a low density expansion up to the order
e^4 n^2 and, additionally, including ladder type contributions via the bound
states in the case of strong magnetic fields (2.35*10^{5} T << B << 2.35*10^{9}
T). We show that for high densities (n=10^{27-30} m^{-3}) and temperatures
T=10^5 - 10^6 K typical for the surface of neutron stars nonideality effects
as, e.g., Debye screening must be taken into account.
