Classical Spin Liquid: Exact Solution for the Infinite-Component Antiferromagnetic Model on the Kagom\'e Lattice

TL;DR

This paper provides an exact analytical solution for the classical antiferromagnetic spin model on the kagomé lattice in the infinite-component limit, revealing how correlations decay and how thermodynamic properties behave.

Contribution

It introduces an exact solution for the infinite-component spin-vector model on the kagomé lattice, capturing the effects of fluctuations and degeneracy.

Findings

Correlations decay at the lattice scale due to ground state degeneracy.

Spin correlation functions decay as 1/r^2 at low temperatures.

Analytical results agree well with Monte Carlo simulations.

Abstract

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.