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The concept of exponential growth in the number of states was originally proposed in the context of condensed matter physics. It was incorporated into high-energy physics in mid 1960. In hadronic physics, the Hagedorn temperature is today understood to be the deconfinement temperature of quarks, while in string theory, it indicates another phase transition: the transition at which very long strings are copiously produced. It is controlled by the size of the string tension which is smaller than the Planck scale by the some power of the coupling constant. By adjusting the tension to be small compared to the Planck scale, the Hagedorn transition can be much less than the Planck temperature. Traditional grand-unified string models place this in the magnitude of 1030 kelvin, two orders of magnitude smaller than the Planck temperature.
Read more about this topic: Hagedorn Temperature
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