Logo image
Small Numerators Canceling Small Denominators: Is Dyson's Hierarchical Model Solvable?
Journal article   Open access   Peer reviewed

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

Y Meurice
Physical review. E, Statistical, nonlinear, and soft matter physics, Vol.63(5), pp.551011-551014
08/05/2000
DOI: 10.1103/PhysRevE.63.055101
url
https://arxiv.org/pdf/cond-mat/0008087View
Open Access

Abstract

Phys.Rev. E63 (2001) 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.

Details

Metrics

Logo image