Hierarchical model of a vector ferromagnet. Selfsimilar block-spin distributions and the Lee-Yang theorem. (English) Zbl 0679.60107
Summary: For a translationally invariant model of a vector ferromagnet the approximating model possessing hierarchical structure is constructed. The equation for self-similar distributions of block-spins in the hierarchical model is investigated in the framework of suitable function theory methods. In particular, the generalised Lee-Yang theorem is proved for arbitrary block-spin dimensionalities.
MSC:
| 60K35 | Interacting random processes; statistical mechanics type models; percolation theory |
| 82B31 | Stochastic methods applied to problems in equilibrium statistical mechanics |
References:
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