  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, $D \to \infty$. In contrast to
conventional two-dimensional magnets with continuous symmetry showing extended
short-range order at distances smaller than the correlation length, $r \lesssim
\xi_c \propto \exp(T^*/T)$, 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
$<{\bf S}_0 {\bf S}_r > \propto 1/r^2$ in the range $a_0 \ll r \ll \xi_c
\propto T^{-1/2}$, where $a_0$ 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 the
infinite-component spin vector model on the checkerboard lattice is a classical
spin liquid.
