First-Order Vortex Lattice Melting in Bilayer Ice: A Monte Carlo Method Study

Inspired by the stable bilayer water ice grown in the laboratory (Nature 577, 60, 2020), we propose a model representing water ice as a two-layer six-vertex model. Using the loop update Monte Carlo method, we unveil meaningful findings. While the square lattice six-vertex model exhibits an antiferromagnetic to disordered phase transition known as the Berezinskii-Kosterlitz-Thouless transition, we observe a different scenario for the bilayer six-vertex model, where the transition type transforms into an Ising transition. We discover the emergence of vortices in the disordered phase, and to stabilize them, vortex excitation is induced. This leads to the presence of distinct 1/2 filling and 2/3 filling vortex lattice phases. Importantly, we identify the phase transitions between the vortex lattice phase and the disorder phase, as well as between the 1/2 and 2/3 vortex lattices, as being of first order. Our findings provide valuable insights into the nature of phase transitions occurring in layered water ice and artificial spin ice systems in experimental setups.