Classical antiferromagnets on the Kagomé lattice

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 n>3 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{→}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{→}0. Thus we argue that the Heisenberg model has long-range antiferromagnetic order in the limit T{→}0. For n>3 the system appears to remain disordered for T{→}0.