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

Thermodynamic quantities and correlation functions (CF's) of the classical antiferromagnet on the kagom\'e lattice are studied for the exactly solvable infinite-component spin-vector model, →D∞. 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, rξc∝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 CF's decay as 〈S₀Sᵣ〉∝1/r² in the range a₀rξc∝T^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are in fairly good quantitative agreement with the Monte Carlo simulations for the classical Heisenberg model, $D=3.$ The neutron-scattering cross section has its maxima beyond the first Brillouin zone; at →T0 it becomes nonanalytic but does not diverge at any q.