Non-intersection exponents of fully packed trails on the square lattice

Yacine Ikhlef (1, 2) , Jesper Lykke Jacobsen (1, 2) , Hubert Saleur (2, 3)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
2 SPhT - Service de Physique Théorique
3 Department of Physics and Astronomy [USC, Los Angeles]

Fully packed trails on the square lattice are known to be described, in the long distance limit, by a collection of free non compact bosons and symplectic fermions, and thus exhibit some properties reminiscent of Brownian motion, like vanishing fuseau exponents. We investigate in this paper the situation for their non-intersection exponents. Our approach is purely numerical, and based both on transfer matrix and Monte Carlo calculations. We find some evidence for non-intersection exponents given by CFT formulas similar to the Brownian case, albeit slightly different in their details.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Yacine Ikhlef, Jesper Lykke Jacobsen, Hubert Saleur. Non-intersection exponents of fully packed trails on the square lattice. Journal of Statistical Mechanics: Theory and Experiment, 2007, pp.P05005. ⟨hal-00119655v2⟩