String bits at finite temperature and the Hagedorn phase

We study the behavior of a simple string bit model at finite temperature. We use thermal perturbation theory to analyze the high temperature regime. But at low temperatures we rely on the large N limit of the dynamics, for which the exact energy spectrum is known. Since the lowest energy states at infinite N are free closed strings, the N = infinity partition function diverges above a finite temperature beta(-1)(H), the Hagedorn temperature. We argue that in these models at finite N, which then have a finite number of degrees of freedom, there can be neither an ultimate temperature nor any kind of phase transition. We discuss how the discontinuous behavior seen at infinite N can be removed at finite N. In this resolution the fundamental string bit degrees of freedom become more active at temperatures near and above the Hagedorn temperature.