Enhanced Gr\"uneisen Parameter in Supercooled Water

We use the recently-proposed \emph{compressible cell} Ising-like model [Phys. Rev. Lett. \textbf{120}, 120603 (2018)] to estimate the ratio between thermal expansivity and specific heat (the Gr\"uneisen parameter $\Gamma$) in supercooled water. Near the critical pressure and temperature, $\Gamma$ increases. The $\Gamma$ value diverges near the pressure-induced finite-$T$ critical end-point [Phys. Rev. Lett. \textbf{104}, 245701 (2010)] and quantum critical points [Phys. Rev. Lett. \textbf{91}, 066404 (2003)], which indicates that two energy scales are governing the system. This enhanced behavior of $\Gamma$ is caused by the coexistence of high- and low-density liquids [Science \textbf{358}, 1543 (2017)]. Our findings support the proposed liquid-liquid critical point in supercooled water in the No-Man's Land regime, and indicates possible applications of this model to other systems.