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

Thermodynamic quantities and correlation functions (CF’s) of the classical antiferromagnet on the kagomé lattice are studied for the exactly solvable infinite-component spin-vector model, $\overrightarrow{D}\infty .$ 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, $r\lesssim {\xi }_c\propto \exp {(T}^{*}/T),$ correlations in the kagomé-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 $〈{\mathbf{S}}_0{\mathbf{S}}_r〉\propto {1/r}^2$ 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 in fairly good quantitative agreement with the Monte Carlo simulations for the classical Heisenberg model, $D=3.\mathrm{}$ The neutron-scattering cross section has its maxima beyond the first Brillouin zone; at $\overrightarrow{T}0$ it becomes nonanalytic but does not diverge at any $\mathbf{q}.$