Variant Monte Carlo algorithm for driven elastic strings in random media

TL;DR

This paper proves key properties of the Variant Monte Carlo algorithm for driven elastic strings in disordered media, demonstrating its advantages over local methods in accurately studying depinning thresholds.

Contribution

The paper establishes theoretical proofs that confirm the no-passing rule and forward-only movement of the algorithm, enhancing its reliability in depinning studies.

Findings

Proves the no-passing rule for the algorithm

Shows the string moves only forward after initial time

Demonstrates the algorithm's effectiveness over local methods

Abstract

We discuss the non-local Variant Monte Carlo algorithm which has been successfully employed in the study of driven elastic strings in disordered media at the depinning threshold. Here we prove two theorems, which establish that the algorithm satisfies the crucial no-passing rule and that, after some initial time, the string exclusively moves forward. The Variant Monte Carlo algorithm overcomes the shortcomings of local methods, as we show by analyzing the depinning threshold of a single-pin problem.