Conformal invariance of loop ensembles under Kardar-Parisi-Zhang dynamics

Xiangyu Cao 1 Alberto Rosso 1 Raoul Santachiara 1

EPL, European Physical Society, 2015, 111, pp.16001

We study scaling properties of the honeycomb fully packed loop ensemble associated with a lozenge tiling model of rough surface, when the latter is driven out of equilibrium by Kardar-Parisi-Zhang (KPZ) type dynamics. We show numerically that conformal invariance and signatures of critical percolation appear in the stationary KPZ state. In terms of the two-component Coulomb gas description of the Edwards-Wilkinson stationary state, our finding is understood as the invariance of one component under the effect of the non-linear KPZ term. On the other hand, we show a breaking of conformal invariance when the level lines of the other component are considered.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques