We show that the thermodynamic limit of the ground state energy in the mixed $p$-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.
"Parisi formula for the ground state energy in the mixed $p$-spin model." Ann. Probab. 45 (6B) 4617 - 4631, November 2017. https://doi.org/10.1214/16-AOP1173