Multispin interactions for multistate spin models

Hendrik Moraal

Physica A: Statistical Mechanics and its Applications, 2000, vol. 285, issue 3, 433-447

Abstract: The multispin interactions for spin models with a transitive symmetry group and M states are considered. It is shown that the triangle-symmetric three-spin interactions depend only on the orbits in the set of all true triangles under the action of the symmetry group; this is analogous to the pair interaction case, which only depends on the orbits in the set of all edges. For four-spin interactions, no such property is shown to hold. The three-spin interactions for all spin models with a completely permissible symmetry group are listed for M⩽10. As an application, a dual transformation for the triangular lattice with a three-spin interaction in half of the triangles is studied; it is shown that this is formally the same as the dual transformation on the square lattice for a special type of group associated with the three-spin interaction. Solutions for the self-dual parts of the state space are outlined for a number of models, yielding information on the points, where a star-triangle transformation is exact.

Date: 2000
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843710000251X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:285:y:2000:i:3:p:433-447

DOI: 10.1016/S0378-4371(00)00251-X

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().