Volume 10, Issue Supplement 2, December 2003, Pages 119 - 132
Polynomial Growth for Birational Mappings from Four-State Spin Edge Models
Available Online 1 December 2003.
- https://doi.org/10.2991/jnmp.2003.10.s2.11How to use a DOI?
- 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.
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Cite this article
TY - JOUR AU - J-M Maillard PY - 2003 DA - 2003/12 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 - https://doi.org/10.2991/jnmp.2003.10.s2.11 ID - Maillard2003 ER -