Polynomial Growth for Birational Mappings from Four-State Spin Edge Models

DOI

10.2991/jnmp.2003.10.s2.11How to use a DOI?

Abstract

We classify all four-state spin edge models according to their behavior under a specific group of birational symmetry transformations generated from the so-called inversion relations. This analysis uses the measure of complexity of the action of birational symetries of these lattice models, and aims at uncovering (star-triangle) solvable ones. One finds that these spin edge models have birational symmetries with a polynomial growth of the iteration calculations. We obtain an unexpected elliptic parametrization of the four-state chiral Potts model, as well as simple, and well-defined, examples of "transcendental" integrability compatible with this polynomial growth of the itertion calculations. As a byproduct we also obtain several homogeneous polynomial representation of the relative integers Z together with their multiplication.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - JOUR
AU  - J-M Maillard
PY  - 2003
DA  - 2003/12/01
TI  - Polynomial Growth for Birational Mappings from Four-State Spin Edge Models
JO  - Journal of Nonlinear Mathematical Physics
SP  - 119
EP  - 132
VL  - 10
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2003.10.s2.11
DO  - 10.2991/jnmp.2003.10.s2.11
ID  - Maillard2003
ER  -