Exact Speed of Sound for all $T$, $\mu$ at Large $N$

We calculate the exact speed of sound for all $T$, $\mu$ in the large $N$ limit for the Gross-Neveu (GN) model in 2+1 dimensions utilizing a non-perturbative field theory technique. At large $N$, the GN model has a chiral symmetric and broken phase separated by a cross-over and critical point at $T=0$. We discuss the behavior of the speed of sound in the whole $T,\mu$ plane numerically without any approximations or conjectures (except for large $N$). We find that the speed of sound displays non-monotonic behavior and exhibits a discontinuity across the critical line. If time allows, potential lessons for QCD will be discussed.