Spin-½ Lattice System: Group Structure and Duality Relation

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Abstract
Properties of general lattice systems are investigated using the group properties of such systems. The duality transformation is generalized and is expressed in terms of exact short sequence between the groups associated with one lattice and the groups associated with the dual lattice. A general method is given for constructing explicitly a dual lattice for any lattice system and is illustrated with some two‐ and three‐dimensional models. In particular it is shown that the two‐dimensional triangular lattice with three‐body forces is self‐dual.