title: Small numerators canceling small denominators: is Dyson's hierarchical model solvable?
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 small denominators as in perturbative expansions near integrable systems in Hamiltonian mechanics. However, in 36 cases considered, a zero denominator always comes with a zero numerator. We conjecture that these cancellations occur in general, allowing the application of the analytical method and suggesting that the model has remarkable features reminiscent of the integrable systems.
authors: Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242, USA.
authors: Y
authors: Y
authors: Meurice