Enhanced Gr\"uneisen Parameter in Supercooled Water

We use the recently-proposed \emph{compressible cell} Ising-like model [Phys. Rev. Lett. $\mathbf{\text{120}}$, 120603 (2018)] to estimate the ratio between thermal expansivity and specific heat (the Gr"uneisen parameter $\mathrm{\Gamma }$) in supercooled water. Near the critical pressure and temperature, $\mathrm{\Gamma }$ increases. The $\mathrm{\Gamma }$ value diverges near the pressure-induced finite-$T$ critical end-point [Phys. Rev. Lett. $\mathbf{\text{104}}$, 245701 (2010)] and quantum critical points [Phys. Rev. Lett. $\mathbf{\text{91}}$, 066404 (2003)], which indicates that two energy scales are governing the system. This enhanced behavior of $\mathrm{\Gamma }$ is caused by the coexistence of high- and low-density liquids [Science $\mathbf{\text{358}}$, 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.