String Bits at Finite Temperature and the Hagedorn Phase

TL;DR

This paper investigates the finite temperature behavior of a string bit model, revealing that the Hagedorn divergence at infinite N is smoothed out at finite N, affecting string activity near the Hagedorn temperature.

Contribution

It demonstrates how finite N models avoid the Hagedorn phase transition, providing insights into string dynamics and thermodynamics at finite degrees of freedom.

Findings

Divergence at Hagedorn temperature is absent at finite N.

Finite N models lack a true phase transition.

String bits become more active near the Hagedorn temperature.

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.