A semiclassical analysis of order from disorder

In this paper we present several examples of order due to disorder phenomena and mainly focus on the Heisenberg antiferromagnet with nearest, neighbour interactions on the Husimi cactus, a system which locally has the same topology as the Kagome lattice. This system has a huge classical degeneracy corresponding to an extensive number of degrees of freedom. We show that unlike thermal fluctuations, quantum fluctuations partially lift this degeneracy and favour a discrete subset of classical ground states. In order to clarify the origin of these effects, we have set up a general semiclassical analysis of the order from disorder phenomenon and clearly identified the differences between classical and quantum fluctuations, This semiclassical approach also enables us to classify various situations where a selection mechanism still occurs. Moreover, once a discrete set of ground states has been preselected, our analysis suggests that tunelling processes within this set should be the dominant effect underlying the strange low-energy spectrum of Kagome-like lattices.