Gluonic mass spectrum in the Abelian bag model

We consider noninteracting gluons confined in a bag whose volume is proportional to its energy. The asymptotic mass spectrum $\rho \mathrm{}\left(m\right)\mathrm{}$ for such a system is derived analytically taking the finite size of the bag into account. The exponent in the mass spectrum is shown to be $\frac{m}{T_0}-\eta {\left(\frac{m}{T_0}\right)}^{\frac{1}{3}}$, where $T_0$ is the limiting temperature and $\eta$ is a shape-dependent positive number. Numerical comparison with exact calculations is made for one specific shape. It is pointed out that the curvature correction term in the exponent has important thermodynamic implications.