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تسجيل مستخدم جديدBirational Mappings and Matrix Sub-algebra from the Chiral Potts Model
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نشر من قبل
Jean-Christian Angl\\`es d'Auriac
تاريخ النشر
2008
مجال البحث
فيزياء
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English
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We study birational transformations of the projective space originating from lattice statistical mechanics, specifically from various chiral Potts models. Associating these models to emph{stable patterns} and emph{signed-patterns}, we give general results which allow us to find emph{all} chiral $q$-state spin-edge Potts models when the number of states $q$ is a prime or the square of a prime, as well as several $q$-dependent family of models. We also prove the absence of monocolor stable signed-pattern with more than four states. This demonstrates a conjecture about cyclic Hadamard matrices in a particular case. The birational transformations associated to these lattice spin-edge models show complexity reduction. In particular we recover a one-parameter family of integrable transformations, for which we give a matrix representation
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