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Small Numerators Canceling Small Denominators: Is Dyson's Hierarchical Model Solvable?

Y. Meurice
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Abstract

We present an analytical method to solve Dyson's hierarchical model, involving the scaling variables near the high-temperature fixed point. The procedure seems plagued by the presence of small denominators as in perturbative expansions near integrable systems in Hamiltonian mechanics. However, in all cases considered, a zero denominator always comes with a zero numerator. We conjecture that these cancellations occur in general, suggesting that the model has remarkable features reminiscent of the integrable systems.

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Y. Meurice. 2000-08-05. Small Numerators Canceling Small Denominators: Is Dyson's Hierarchical Model Solvable?. https://doi.org/10.1103/physreve.63.055101

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