Atlantis Press Paper Details: Polynomial Growth for Birational Mappings from Four-State Spin Edge Models

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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title:		Polynomial Growth for Birational Mappings from Four-State Spin Edge Models
publication:		JNMP
volume-issue:		10 - Supplement 2
pages:		119 - 132
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.2003.10.s2.11 (how to use a DOI)
author(s):		J-M MAILLARD
publication date:		December 2003
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:		© Atlantis Press. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		10s2_10.pdf (171 K)