String Bits at Finite Temperature and the Hagedorn Phase

Abstract

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 $N=\infty$ partition function diverges above a finite temperature ${\beta }_H^{-1}$, 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.

14 pages, 4 figures, typos corrected

References in corpus (3)

• String Gas Cosmology after Planck
• Space from String Bits
• Stable String Bit Models

Cited by in corpus (6)

• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Hagedorn Temperature in Superstring Bits and SU(N) Characters
• Color Characters for White Hot String Bits
• Thermal properties of a string bit model at large N
• A New Census of the Universe's Entropy
• Finite N corrections to white hot string bits