The crystal form of 3D water ice has a highly degenerate ground state, that grows exponentially with the system size. This growth of degeneracy is caused by the number of configurations conforming to the so called "two-in, two-out" ice rule, where all configurations conforming to that rule are symmetric.

A simplified model which approximately obeys the ice rule and is easier to investigate experimentally at the single-particle level is given by 2D artificial square ice.  In this model, symmetry is broken and the ground-state entropy vanishes.

We suggest a new model of sheared square ice. Its uniqueness is in partially restoring the degeneracy.

When shearing the lattice, the second energy level split. Thus, a new energy gap between the two lowest levels emerges. We analytically calculated the energy levels and identified that this new gap between the two lowest energy states becomes relatively small as the shear angle increases.

Following that we performed Monte Carlo simulations and observed that at temperatures corresponding to thermal energies larger than this energy gap, this gap becomes negligible, and occupations of the two almost degenerate states are comparable, leading to a new phase with sub-extensive entropy.

We obtained our results specifically for interactions characteristic of colloids. Nevertheless, the sheared lattice model can be implemented in different systems with a separation of energy scales, e.g., colloids in optical traps, lithographically fabricated ferromagnetic islands.