I think Gates is confusing references here. The behavior he is referring to is a result of
Gross and Mende on scattering of strings at energies above the Planck scale. What they found was that such processes are dominated by a specific string configuration, which could be described as a surface. If you compute the scale ##x_s## associated with the size of the surface (say as the square root of the surface area), you find that it scales with the energy of the process ##x_s \sim l_s^2 E ##, where ##l_s## is the fundamental length present in the string theory. This means that for energies ##E > l_s^{-1}##, our probes actually get larger than the fundamental scale ##l_s## that we would hope to probe. It is actually impossible to measure distances smaller than around ##l_s## with strings, leading to the concept of a minimal distance. This is discussed, along with other evidence, in
this conference talk by Gross, specifically on pages 20-21.
The famous result by Gross and Periwal is
this paper that shows that string perturbation theory is incomplete. Such a result on perturbation theory is interpreted (for example in QCD) as signaling the existence on nonperturbative phenomena. It was subsequently discovered that these phenomena could be described by D-branes. It is actually true that D-branes allow us to probe somewhat shorter distances than fundamental strings (see for example
Shenker), but I do not think that this is what Gates meant (or at least it would not be a result to credit to Gross-Periwal).
Neither of these Gross et al results should really be called a phase transition, but there is a related concept called the
Hagedorn transition. This is a rather technical subject, but in the context of strings, it has been interpreted as a phase transition at a high temperature, beyond which very large strings are produced. This is somewhat reminiscent of the Gross-Mende behavior, where large strings are also the dominant configuration at high energies.