Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions

TL;DR

This study uses advanced multi-surface coding to simulate the RSOS surface growth model in four dimensions, revealing that four dimensions are not the upper critical dimension through finite-size scaling analysis.

Contribution

It introduces a multi-surface coding approach enabling large-scale simulations of the RSOS model in four dimensions, providing new insights into its critical behavior.

Findings

Finite-size scaling analysis shows d=4 is not the upper critical dimension.

Simulations achieved system sizes up to 256^4.

Results suggest different critical behavior than previously assumed.

Abstract

We study the Restricted Solid on Solid (RSOS) model for surface growth in spatial dimension d=4 by means of a multi-surface coding technique that allows to analyze samples to analyze samples of size up to $256^4$ in the steady state regime. For such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations. A careful finite-size scaling analysis of the critical exponents clearly indicate that d=4 is not the upper critical dimension of the model.