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

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

2000-08-05

arxiv.org/abs/cond-mat/0008087v1

Phys.Rev. E63 (2001) 055101

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figs. uses revtex

Scientific paper

10.1103/PhysRevE.63.055101

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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