A Semi-Classical Analysis of Order from Disorder

Details A Semi-Classical Analysis of Order from Disorder A Semi-Classical Analysis of Order from Disorder

1998-02-19

arxiv.org/abs/cond-mat/9802212v1

Physics

Condensed Matter

Statistical Mechanics

49 pages, Latex, 12 PS figures

Scientific paper

10.1088/0305-4470/31/28/005

We study in this paper the Heisenberg antiferromagnet with nearest neighbours interactions on the Husimi cactus, a system which has locally the same topology as the Kagom\'e 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 lift partially 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 semi-classical analysis of the order from disorder phenomenon and clearly identified the differences between classical and quantum fluctuations. This semi-classical 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 Kagom\'e-like lattices.

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