Small Numerators Canceling Small Denominators: Is Dyson's Hierarchical Model Solvable?
Statistical Mechanics
2009-10-31 v1 High Energy Physics - Theory
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.cond-mat/0008087,
title = {Small Numerators Canceling Small Denominators: Is Dyson's Hierarchical Model Solvable?},
author = {Y. Meurice},
journal= {arXiv preprint arXiv:cond-mat/0008087},
year = {2009}
}
Comments
4 pages, 3 figs. uses revtex