Absence of Non-commutative Matrix Observables for q-State Potts Models

C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (1) 2017, pp. 36-44

March 31, 2017

James McVittie<\b>,The Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, Canada H3A 0B9; e-mail: james.mcvittie@mail.mcgill.ca<\em>

Abstract/Résumé:

This article is an expository work introducing the subject of lattice models in statistical physics and the types of observables that can be used to prove convergence, as well as a proof for the q-state Potts model showing that non-commutative matrix observables do not exist.
Cet article est une introduction au sujet des modèles sur réseau en physique statistique et les types d’observables qui peuvent être utilisées pour démontrer la convergence, et aussi une démonstration qu’il n’existe pas d’observable matricielle non-commutative pour le modèle “q-state Potts”.

Keywords: Ising model, Potts model, lattice, matrix, noncommutative, observable
AMS Subject Classification: Dynamics of random walks; random surfaces; lattice animals; etc., Dynamics of disordered systems (random Ising systems; etc.) 82C41, 82C44

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