  We investigate the thermodynamics of a self-interacting relativistic charged
scalar field in the presence of weak disorder. We consider quenched disorder
which couples linearly to the mass of the scalar field. After performing noise
averages over the free energy of the system, we find that disorder increases
the mean-field critical temperature for Bose-Einstein condensation at finite
density. The effect of disorder on the temperature dependence of the chemical
potential for a fixed charge density is investigated. Significant differences
from the mean-field temperature dependence of the chemical potential are
observed as the strength of the noise intensity increases. Finally, the
temperature dependence of the chemical potential with fixed total charge and
entropy is investigated. It is found that there is no Bose-Einstein
condensation for a fixed charge to entropy ratio in the presence of weak
disorder. The possible relevance of the findings in the present paper in
different areas is discussed.
