Topological effects and conformal invariance in long-range correlated random surfaces

Nina Javerzat (1) , Sebastian Grijalva (1) , Alberto Rosso (1) , Raoul Santachiara (1)

1 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

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}

Mots clés: invariance: conformal; field theory: conformal; effect: topological; correlation: long-range; tensor: energy-momentum; cluster; site; percolation; surface; critical phenomena; universality; lattice; torus; random surface; integrability; anisotropy; structure; scaling; fractal; family

Domaines: Physique Générale [physics.gen-ph]

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