Edge correlation function of the 8-vertex model when a+c=b+d
Annales de l’Institut Henri Poincaré D, Tome 5 (2018) no. 4, pp. 557-619.

This paper is devoted to the 8-vertex model and its edge correlation function. In some particular (integrable) cases, we find a closed form of the edge correlation function and we deduce also its asymptotics. In addition, we quantify influence of boundary conditions on this function.

To do this, we introduce a system of particles in interaction related to the 8-vertex model. This system, studied using various tools fromanalytic combinatorics, random walks and conics, permits to compute the correlation function. To study the influence of boundary conditions, we involve probabilistic cellular automata of order 2.

Accepté le :
Publié le :
DOI : 10.4171/aihpd/63
Classification : 82-XX, 05-XX, 60-XX
Mots-clés : 8-vertex model, correlation function, system of particles, probabilistic cellular automata 
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     author = {Casse, J\'er\^ome},
     title = {Edge correlation function of the 8-vertex model when $a + c = b + d$},
     journal = {Annales de l{\textquoteright}Institut Henri Poincar\'e D},
     pages = {557--619},
     volume = {5},
     number = {4},
     year = {2018},
     doi = {10.4171/aihpd/63},
     mrnumber = {3900291},
     zbl = {1406.82006},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/aihpd/63/}
}
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Casse, Jérôme. Edge correlation function of the 8-vertex model when $a + c = b + d$. Annales de l’Institut Henri Poincaré D, Tome 5 (2018) no. 4, pp. 557-619. doi : 10.4171/aihpd/63. http://www.numdam.org/articles/10.4171/aihpd/63/

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