Classical Spin Liquid Properties of a Fully Frustrated Two Dimensional Lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D → ∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ∼ ξc ∝ exp(T /T ), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as 〈S0Sr〉 ∝ 1/r 2 in the range a0 ≪ r ≪ ξc ∝ T , where a0 is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of this model on the checkerboard lattice is a classical spin liquid and that the checkerboard lattice is a good two dimensionnal approximation for the pyrochlore lattice.