Classical antiferromagnets on the Kagomé lattice.

TLDR: It is argued that the Heisenberg model has long-range antiferromagnetic order in the limit T 0, and the system appears to remain disordered for T 0.

Abstract: We examine the classical antiferromagnet on the Kagom\'e lattice with nearest-neighbor interactions and n-component vector spins. Each case n=1,2,3 and ng3 has its own special behavior. The Ising model (n=1) is disordered at all temperatures. The XY model (n=2) in the zero-temperature (T\ensuremath{\rightarrow}0) limit reduces to the three-state Potts model, which in turn can be mapped onto a solid-on-solid model that is o/Iat its roughening transition. Exact critical exponents are derived for this system. The spins in the Heisenberg model (n=3) become coplanar and more ordered than the XY model as T\ensuremath{\rightarrow}0. Thus we argue that the Heisenberg model has long-range antiferromagnetic order in the limit T\ensuremath{\rightarrow}0. For ng3 the system appears to remain disordered for T\ensuremath{\rightarrow}0.