CLASSICAL ANTIFERROMAGNETS ON THE KAGOME LATTICE

We examine the classical antiferromagnet on the Kagome 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 at 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.