A MODEL OF INTERACTING STRINGS AND THE HAGEDORN PHASE-TRANSITION

In this letter we introduce a model of interacting strings in which the usual ideal gas approximations are not made. The model is constructed in analogy with nucleation models, the formation of droplets in a supersaturated gas. We consider the strings to be interacting and their number not fixed. The equilibrium configuration is the one for which the time derivative of the number of strings in the various energies vanishes. We evaluate numerically the equilibrium configurations for various values of the energy density. We find that at a density of order one in Planck units there is a sharp transition, from a "gas" phase in which there are many strings, all in the massless or first few excited states, to a "liquid" phase in which all strings have coalesced into one (or few) highly excited string. © 1990.