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 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.

4 pages, 3 figs. uses revtex

References in corpus (3)

• Renormalization group flow of SU(3) lattice gauge theory - Numerical studies in a two coupling space
• Non-Universal Quantities from Dual RG Transformations
• Hyperscaling in the Broken Symmetry Phase of Dyson's Hierarchical Model

Cited by in corpus (2)

• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model
• Small numerators canceling small denominators of the high-temperature scaling variables: a systematic explanation in arbitrary dimensions