  The spherical Sherrington-Kirkpatrick (SSK) model and its bipartite analog
both exhibit the phenomenon that their free energy fluctuations are
asymptotically Gaussian at high temperature but asymptotically Tracy-Widom at
low temperature. This was proved in two papers by Baik and Lee, for all
non-critical temperatures. The case of critical temperature was recently
computed for the SSK model in two separate papers, one by Landon and the other
by Johnstone, Klochkov, Onatski, Pavlyshyn. In the current paper, we derive the
critical temperature result for the bipartite SSK model. In particular, we find
that the free energy fluctuations exhibit a transition when the temperature is
in a window of size $n^{-1/3}\sqrt{\log n}$ around the critical temperature,
the same window for the SSK model. Within this transitional window, the
asymptotic fluctuations of the free energy are the sum of independent Gaussian
and Tracy-Widom random variables.
