Order by disorder and phase transitions in a highly frustrated spin model on the triangular lattice

Frustration has proved to give rise to an extremely rich phenomenology in both quantum and classical systems. The leading behavior of the system can often be described by an effective model, where only the lowest-energy degrees of freedom are considered. In this paper we study a system corresponding to the strong trimerization limit of the spin 1/2 kagome antiferromagnet in a magnetic field. It has been suggested that this system can be realized experimentally by a gas of spinless fermions in an optical kagome lattice at 2/3 filling. We investigate the low-energy behavior of both the spin 1/2 quantum version and the classical limit of this system by applying various techniques. We study in parallel both signs of the coupling constant J since the two cases display qualitative differences. One of the main peculiarities of the J>0 case is that, at the classical level, there is an exponentially large manifold of lowest-energy configurations. This renders the thermodynamics of the system quite exotic and interesting in this case. For both cases, J>0 and J<0, a finite-temperature phase transition with a breaking of the discrete dihedral symmetry group D_6 of the model is present. For J<0, we find a transition temperature T^<_c/|J| = 1.566 +/- 0.005, i.e., of order unity, as expected. We then analyze the nature of the transition in this case. While we find no evidence for a discontinuous transition, the interpretation as a continuous phase transition yields very unusual critical exponents violating the hyperscaling relation. By contrast, in the case J>0 the transition occurs at an extremely low temperature, T^>_c ~= 0.0125 J. Presumably this low transition temperature is connected with the fact that the low-temperature ordered state of the system is established by an order-by-disorder mechanism in this case.Comment: 18 pages including 18 figures and 1 table; replaced in order to match published version, most important change: added appendix with derivation of Hamiltonian from spin-1/2 Heisenberg model on trimerized kagome lattic

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^\circ spin structure. To determine the transition temperature, we perform Monte-Carlo simulations and measure specific heat, 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^\circ spin-structure. A finite but very small transition temperature is detected by Monte-Carlo simulations using the exchange method.Comment: 11 pages including 9 figures, uses IOP style files; to appear in J. Phys.: Condensed Matter (proceedings of HFM2006