Determination of the melting temperature of hexagonal ice using Lee-Yang phase transition theory

Lee-Yang phase transition theory is a milestone in statistical physics. Its applications in realistic systems, however, had been substantially hindered by availability of practical schemes to calculate the Lee-Yang zeros. In this manuscript, we extend the scheme we have designed earlier [Phys. Rev. E 109, 024118 (2024)] and report simulation results for the melting temperature $(T)$ of ice Ih under ambient pressure $(p)$. The enhanced sampling technique is shown to be crucial for accessing Lee-Yang zeros accurately. The real and imaginary parts of the Lee-Yang edges exhibit linear finite-size scaling, yielding an extrapolated melting $T$ of 274.70 K for the mW water potential in the thermodynamic limit. This result agrees quantitatively with prior coexistence simulations, while offering a significant reduction in computational cost: the phase boundary can be determined from a single simulation even when performed distant from actual transition conditions, unlike conventional methods that require multiple simulations scanning $T$ or $p$. With these, we demonstrate the applicability of Lee-Yang phase transition theory in realistic molecular systems and provide a feasible scheme for high-throughput calculations in determining the phase transition temperature.