Finite-temperature ordering in a two-dimensional highly frustrated spin model

We investigate the classical counterpart of an effective Hamiltonian for a strongly trimerized kagome lattice. Although the Hamiltonian only has a discrete symmetry, the classical groundstate manifold has a continuous global rotational symmetry. Two cases should be distinguished for the sign of the exchange constant. In one case, the groundstate has a 120° spin structure. To determine the transition temperature, we perform Monte Carlo simulations and measure specific the heat and the order parameter as well as the associated Binder cumulant. In the other case, the classical groundstates are macroscopically degenerate. A thermal order-by-disorder mechanism is predicted to select another 120° spin structure. A finite but very small transition temperature is detected by Monte Carlo simulations using the exchange method.