Glazman, Alexander Manolescu, Ioan 2020-11-01 We consider a self-avoiding walk model (SAW) on the faces of the square lattice Z2. This walk can traverse the same face twice, but crosses any edge at most once. The weight of a walk is a product of local weights: each square visited by the walk yields a weight that depends on the way the walk passes through it. The local weights are parametrised by angles θ∈[π3,2π3] and satisfy the Yang–Baxter equation. The self- avoiding walk is embedded in the plane by replacing the square faces of the grid with rhombi with corresponding angles.By means of the Yang–Baxter transformation, we show that the 2-point function of the walk in the half-plane does not depend on the rhombic tiling (i.e. on the angles chosen). In particular, this statistic concides with that of the self-avoiding walk on the hexagonal lattice. Indeed, the latter can be obtained by choosing all angles θ equal to π3.For the hexagonal lattice, the critical fugacity of SAW was recently proved to be equal to 1+2–√. We show that the same is true for any choice of angles. In doing so, we also give a new short proof to the fact that the partition function of self-avoiding bridges in a strip of the hexagonal lattice tends to 0 as the width of the strip tends to infinity. This proof also yields a quantitative bound on the convergence. application/pdf https://folia.unifr.ch/global/documents/309306 https://folia.unifr.ch/documents/309306/files/man_saw.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.1214/19-AIHP1024 info:eu-repo/semantics/openAccess License undefined Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. - 2020, vol. 56, no. 4, p. 2281–2300 info:eu-repo/classification/udc/51 Self-avoiding walk on $\mathbb{Z}^{2}$ with Yang–Baxter weights : Universality of critical fugacity and 2-point function http://purl.org/coar/resource_type/c_6501