Interpretation of the symmetry group of the homogeneous 16-vertex model in terms of Lorentz similarity transformations

A. Gaaff and J. Hijmans

Physica A: Statistical Mechanics and its Applications, 1978, vol. 94, issue 2, 192-210

Abstract: A new analysis is made of the symmetry group of the general homogeneous 16-vertex model on a square lattice, i.e. the group of transformations in the parameter space of the model leaving invariant its partition function. The set of 16 vertex weights is decomposed in such a way that the ensuing matrix P of 16 composite parameters transforms according to the group of Lorentz similarity transformations. Equivalence classes of models can be characterized by a suitably chosen ‘normal’ matrix P(n), depending on 10 parameters, four having the significance of principle values, and the remaining six (two angles and two 3-dimensional unit vectors) determining a Lorentz transformation. The analysis is applied to the general eight-vertex model as well as to its soluble subclasses, the symmetric eight-vertex model, the general six-vertex model and the free fermion model.

Date: 1978
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:94:y:1978:i:2:p:192-210

DOI: 10.1016/0378-4371(78)90096-1

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