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Multicomponent spin models with transitive symmetry groups

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  • Moraal, H.

Abstract

A general theory for multicomponent spin models with transitive symmetry groups is developed. These symmetry groups are shown to belong to a certain class of “permissible” groups. A number of theorems concerning these groups is proved and large classes of them are explicitly constructed. The statistical mechanics of this type of model is discussed; a detailed derivation for the phase transitions of these models on Cayley trees is given. It is shown that the Ising, Potts, Ashkin-Teller and “clock” models are special cases of larger classes of models of this type. As completely new models, the so-called F-models are defined as models with a nonabelian, regular, permissible symmetry group. For this type of model, the set of all pair energy functions is shown not to form an algebra, which results in unique properties not found for the well-known models and their generalizations, which all possess associated algebras.

Suggested Citation

  • Moraal, H., 1982. "Multicomponent spin models with transitive symmetry groups," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 113(1), pages 44-66.
    • Handle: RePEc:eee:phsmap:v:113:y:1982:i:1:p:44-66
    DOI: 10.1016/0378-4371(82)90004-8
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