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Annales de l’Institut Henri Poincaré D


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Volume 5, Issue 4, 2018, pp. 557–619
DOI: 10.4171/AIHPD/63

Published online: 2018-07-25

Edge correlation function of the 8-vertex model when $a + c = b + d$

Jérôme Casse[1]

(1) Université de Lorraine, Vandoeuvre-lès-Nancy, France

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.

Keywords: 8-vertex model, correlation function, system of particles, probabilistic cellular automata

Casse Jérôme: Edge correlation function of the 8-vertex model when $a + c = b + d$. Ann. Inst. Henri Poincaré Comb. Phys. Interact. 5 (2018), 557-619. doi: 10.4171/AIHPD/63