THE NUCLEATION MODEL OF THE HAGEDORN PHASE-TRANSITION

In this paper we discuss a model of interacting strings at finite densities based on nucleation theory, the study of formation of droplets in a supersaturated gas, the analogy being between drops of various sizes and strings with various excitation number. The interaction of the strings is considered to be the usual merging and splitting. We do not assume equilibrium a priori but find equilibrium configurations of strings as a result of their dynamics. We study these configurations as we change the energy density, and find the presence of two phases. A low-density "gas" phase, in which the energy is in strings in the fundamental or the first few excited levels, and a high-density "liquid" phase in which the number of strings is low, all the energy being carried by a few very excited strings. For the gas phase we also discuss the thermodynamics of the system.