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 hightemperature 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.
 Publication:

Physical Review E
 Pub Date:
 May 2001
 DOI:
 10.1103/PhysRevE.63.055101
 arXiv:
 arXiv:condmat/0008087
 Bibcode:
 2001PhRvE..63e5101M
 Keywords:

 64.60.Ak;
 05.10.Cc;
 05.50.+q;
 11.10.Hi;
 Renormalizationgroup fractal and percolation studies of phase transitions;
 Renormalization group methods;
 Lattice theory and statistics;
 Renormalization group evolution of parameters;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 4 pages, 3 figs. uses revtex