Tricritical systems with long-range interactions

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Abstract
Two elastic spin models with nonclassical tricritical points are discussed. The singular parts of the free energies near the tricritical points have homogeneity properties which must be formulated in terms of curvilinear coordinates, although the linear variables of Griffiths or Riedel may be used more generally than recently noted. One of our models, though not an example of the recent theory of constrained systems, exhibits the same tricritical behavior as these systems. This similarity is explained on the basis of a Curie-Weiss-like four-spin interaction occurring in our models as well as in the constrained spin model of Rudnick, Bergman, and Imry. A more general equation of state for tricritical systems with long-range interactions is suggested.