  We study hydrogen plasmas at magnetic fields B ~ 10^{12}-10^{13} Gauss,
densities ~ 10^{-3}-10^3 g/cc and temperatures T ~ 10^{5.5}-10^{6.5} K, typical
of photospheres of middle-aged cooling neutron stars. We construct an
analytical free energy model of the partially ionized plasma, including into
consideration the decentred atomic states, which arise due to the thermal
motion across the strong field. We show that these states, neglected in
previous studies, may contribute appreciably into thermodynamics of the outer
atmospheric layers at density below 1 g/cc and typical B and T. We take into
account Coulomb non-ideality of the ionized component of the plasma affected by
intense magnetic field. Ionization degree, occupancies and equation of state
are calculated, and their dependences on the temperature, density and magnetic
field are studied.
