Geometric Frustration: Triangular Antiferromagnet

Not all bonds can be satisfied simultaneously — residual frustration persists even at T=0

T = 0.5 Triangular frustration: -
Square frustration: - Energy/bond: -
About: On a triangular lattice, antiferromagnetic Ising spins cannot all be antiparallel — at least one bond in each triangle must be "frustrated" (parallel spins). This geometric frustration prevents ordering even at T=0, leading to a massively degenerate ground state and unusual thermodynamics. In contrast, the square lattice antiferromagnet easily orders (checkerboard pattern). Real frustrated systems include spin ices, pyrochlores, and kagome magnets.