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True nature of long-range order in a plaquette orbital model
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Biskup, Marek and Kotecky, Roman (2010) True nature of long-range order in a plaquette orbital model. Journal of Statistical Mechanics: Theory and Experiment, Vol.2010 (No.11). P11001. doi:10.1088/1742-5468/2010/11/P11001
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Official URL: http://dx.doi.org/10.1088/1742-5468/2010/11/P11001
Abstract
We analyze the classical version of a plaquette orbital model that was recently introduced and studied numerically by Wenzel and Janke. In this model, edges of the square lattice are partitioned into x and z types that alternate along both coordinate directions and thus arrange into a checkerboard pattern of x and z plaquettes; classical O(2) spins are then coupled ferromagnetically via their first components over the x edges and via their second components over the z edges. We prove from first principles that, at sufficiently low temperatures, the model exhibits orientational long-range order (OLRO) in one of the two principal lattice directions. Magnetic order is precluded by the underlying symmetries. A similar set of results is inferred also for quantum systems with large spin although the spin-1/2 instance currently seems beyond the reach of rigorous methods. We point out that the Neel order in the plaquette energy distribution observed in numerical simulations is an artifact of the OLRO and a judicious choice of the plaquette energies. In particular, this order seems to disappear when the plaquette energies are adjusted to vanish at the ground-state level. We also discuss the specific role of the underlying symmetries in Wenzel and Janke's simulations and propose an enhanced method of numerical sampling that could in principle significantly increase the speed of convergence.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Journal of Statistical Mechanics: Theory and Experiment | ||||
| Publisher: | Institute of Physics Publishing Ltd. | ||||
| ISSN: | 1742-5468 | ||||
| Official Date: | November 2010 | ||||
| Dates: |
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| Volume: | Vol.2010 | ||||
| Number: | No.11 | ||||
| Page Range: | P11001 | ||||
| DOI: | 10.1088/1742-5468/2010/11/P11001 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access | ||||
| Funder: | NSF | ||||
| Grant number: | DMS-0949250 (NSF), GACR 201-09-1931, MSM 0021620845 |
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