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Thermodynamic quantities and correlation functions (CFs) of the classicalantiferromagnet on the kagom\'e lattice are studied for the exactly solvableinfinite-component spin-vector model, D \to \infty. In this limit, the criticalcoupling of fluctuations dies out and the critical behavior simplifies, but theeffect of would be Goldstone modes preventing ordering at any nonzerotemperature is properly accounted for. In contrast to conventionaltwo-dimensional magnets with continuous symmetry showing extended short-rangeorder at distances smaller than the correlation length, r < \xi_c \propto\exp(T^*/T), correlations in the kagom\'e-lattice model decay already at thescale of the lattice spacing due to the strong degeneracy of the ground statecharacterized by a macroscopic number of strongly fluctuating local degrees offreedom. At low temperatures, spin CFs decay as <{\bf S}_0 {\bf S}_r> \propto1/r^2 in the range a_0 << r << \xi_c \propto T^{-1/2}, where a_0 is the latticespacing. Analytical results for the principal thermodynamic quantities in ourmodel are in fairly good quantitative agreement with the MC simulations for theclassical Heisenberg model, D=3. The neutron scattering cross section has itsmaxima beyond the first Brillouin zone; at T\to 0 it becomes nonanalytic butdoes not diverge at any q.Comment: 14 PR pages, 10 figures; Phys. Rev. B; Version 3: final published  versio

Classical spin liquid: Exact solution for the infinite-component antiferromagnetic model on thekagomélattice