  In the study of the small ten-dimensional Schwarzschild blackhole, the
blackhole to string transition is an important problem. In hep-th/0605041, a
possible identification is made between the Gross-Witten-Wadia (GWW) type
third-order large-N phase transition in the boundary gauge theory and the
string-black hole transition in the bulk. In this paper, we exhibit the
existence of the GWW transition by Monte Carlo simulation in the zero mode
bosonic action of the finite-temperature N=4 SYM theory on S^3. Exhibiting this
transition in the truncated but highly non-trivial gauge theory implies that in
the vicinity of the critical temperature T_c, the system goes critical, and the
fluctuations give rise to universal formulas derived in hep-th/0605041 We also
discuss the issue of SO(6) R-symmetry breaking.
