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.

Figure 1. Antiferromagnetic Ising on a triangular lattice. Spins are drawn as up/down discs with the fully frustrated (all-equal) triangles flagged in red; the toggle shows the three-sublattice chirality domains instead. The diagnostic tracks the satisfied-bond fraction against its 2/3 ceiling and the magnetization. Method: single-spin Metropolis Monte Carlo.

T0.50

L40

speed3

viewspins

WHAT TO TRY

Cool the lattice (lower T) and watch the red frustrated triangles thin out but never vanish, the visible sign that frustration cannot be fully relieved.
Follow the lower plot: the satisfied-bond fraction rises toward 2/3 and stalls there (one frustrated bond per triangle is unavoidable), while |M| stays near zero, so the lattice never orders.
Switch the view to chirality domains: the salt-and-pepper spins resolve into the three-sublattice domain mosaic, the order that emerges from disorder.
Hit Cold (stripe) then watch it relax, or Hot (random) to quench from infinite temperature.