  Thermodynamic quantities and correlation functions (CFs) of the classical
antiferromagnet on the kagom\'e lattice are studied for the exactly solvable
infinite-component spin-vector model, D \to \infty. In this limit, the critical
coupling of fluctuations dies out and the critical behavior simplifies, but the
effect of would be Goldstone modes preventing ordering at any nonzero
temperature is properly accounted for. In contrast to conventional
two-dimensional magnets with continuous symmetry showing extended short-range
order at distances smaller than the correlation length, r < \xi_c \propto
\exp(T^*/T), correlations in the kagom\'e-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 << r << \xi_c \propto T^{-1/2}, where a_0 is the lattice
spacing. Analytical results for the principal thermodynamic quantities in our
model are in fairly good quantitative agreement with the MC simulations for the
classical Heisenberg model, D=3. The neutron scattering cross section has its
maxima beyond the first Brillouin zone; at T\to 0 it becomes nonanalytic but
does not diverge at any q.
