Year: 2026
Type: article
Abstract: We investigate the behavior of discrete interface growth models belonging to the Edwards–Wilkinson (EW) and Kardar–Parisi–Zhang (KPZ) universality classes, when defined on a complete graph, a topology commonly used to probe the infinite-dimensional limit of statistical mechanical systems. Our aim is to assess to what extent discrete lattice models reproduce the behavior of their corresponding continuum equations in this highly connected setting. After assessing the trivial behavior shown by some well known cases (like random deposition with surface relaxation or the etching model), we focus on two paradigmatic models associated with the KPZ universality class, the restricted solid-on-solid (RSOS) and ballistic deposition (BD) models, and assess non-trivial behavior through several observables including the roughness, height fluctuations, power spectra, and two-time autocorrelation functions. Still, despite similarities with continuum equations, important differences arise in the fluctuations and long-time dynamics. In both discrete models the distribution of rescaled height fluctuations display a pronounced left tail, indicating the presence of lagging nodes. While the RSOS model exhibits a saturation roughness that decreases with system size, similarly to the EW and KPZ equations, at intermediate times the BD model exhibits an ultrafast growth regime that is followed at long times by a time-independent roughness that increases with system size, both in contrast with the behavior of the KPZ equation on a complete graph.
Institutions: Universidad de Extremadura, Universidad Carlos III de Madrid
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Awards: G103507813, G1105844351, G1455481585, G1938719665, G2019505627, G2262748287, G2693832139, G2875277374, G2890270296, G300979063, G3268032660, G3363355534, G3480869486, G3999133987, G410571670, G425668148, G451917667, G4519335756, G491712853, G5080475149, G5539308778, G5635532810, G586857820, G5967599077, G6172591091, G7084143925, G717256432, G7397253025, G7765948776, G7805626310, G7863371703, G8497050386, G986506960
OpenAlex ID: W7159711161