Frustrated triangular antiferromagnet

What you are seeing: antiferromagnetic Ising spins on a 2D triangular lattice. Each spin energetically wants to be opposite to its 6 neighbors, but the triangular geometry makes that impossible: on every elementary triangle, you cannot anti-align all three pairs at once. The system is "frustrated".

Famous result: the 2D AF Ising on a triangular lattice has no phase transition at finite $T$. Even at $T = 0$ the ground state has extensive residual entropy. Watch the lattice: even at very low $T$ it never reaches a clean checkerboard order; instead a sea of competing domains lives forever.