Universal behavior ofD-dimensional superstring models

We derive the asymptotic form ${\mathrm{cm}}^{\mathrm{-}a}$ $e^{\mathrm{bm}}$ of the density of states for general D-dimensional models of open and closed (super)strings. We find the leading behavior to be essentially model independent. It depends only on the (super)reparametrization properties of the world sheet and the value of the string mass scale (the Regge slope). We investigate the thermodynamic behavior of an ‘‘ideal string gas’’ implied by this density of states. Such a system is stable for all open strings as well as for closed strings with D≤3. In this case the Hagedorn temperature $T_H$=1/b is the maximum temperature of the system. An ideal gas of closed strings with D>3 exhibits critical behavior at T=$T_H$ with the space-time dimension D determining the system’s critical-point exponents. The possibility that T=$T_H$ is a multicritical point is also examined.