# Topological effects and conformal invariance in long-range correlated random surfaces – Archive ouverte HAL

### Nina Javerzat 1 Sebastian Grijalva 1 Alberto Rosso 1 Raoul Santachiara 1

#### Nina Javerzat, Sebastian Grijalva, Alberto Rosso, Raoul Santachiara. Topological effects and conformal invariance in long-range correlated random surfaces. SciPost Phys., 2020, 9 (4), pp.050. ⟨10.21468/SciPostPhys.9.4.050⟩. ⟨hal-02863162⟩

We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites is usually denoted as the excursion set. The connected components of this set, the level clusters, define a one-parameter ($H$) family of percolation models with long-range correlation in the site occupation. The level clusters percolate at a finite value $h=h_c$ and for $H\leq-\frac{3}{4}$ the phase transition is expected to remain in the same universality class of the pure (i.e. uncorrelated) percolation. For \$-\frac{3}{4}

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