Space-time correlations of a Gaussian interface

TL;DR

This paper studies the relaxation dynamics of a Gaussian interface model with sub-lattice parallel updates, providing exact results and numerical comparisons to previous continuous-time models, enhancing understanding of space-time correlations.

Contribution

It introduces exact analysis of sub-lattice parallel dynamics for Gaussian interfaces and compares these results to existing continuous-time models.

Findings

Exact relaxation dynamics for sub-lattice parallel Gaussian interfaces

Numerical comparison with continuous-time harness processes

Insights into space-time correlation behaviors

Abstract

The serial harness introduced by Hammersley is equivalent, in the Gaussian case, to the Gaussian Solid-On-Solid interface model with parallel heat bath dynamics. Here we consider sub-lattice parallel dynamics, and give exact results about relaxation dynamics, based on the equivalence to the infinite time limit of a time periodic random field. We also give a numerical comparison to the harness process in continuous time studied by Hsiao and by Ferrari, Niederhauser and Pechersky.