Anchored advected interfaces, Oslo model, and roughness at depinning

Fuente: arXiv
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Auteurs principaux: Shapira, Assaf, Wiese, Kay Joerg
Format: Preprint
Publié: 2023
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author Shapira, Assaf
Wiese, Kay Joerg
author_facet Shapira, Assaf
Wiese, Kay Joerg
contents There is a plethora of 1-dimensional advected systems with an absorbing boundary: the Toom model of anchored interfaces, the directed exclusion process where in addition to diffusion particles and holes can jump over their right neighbor, simple diffusion with advection, and Oslo sandpiles. All these models share a roughness exponent of $ζ=1/4$, while the dynamic exponent $z$ varies, depending on the observable. We show that for the first three models $z=1$, $z=2$, and $z=1/2$ are realized, depending on the observable. The Oslo model is apart with a conjectured dynamic exponent of $z=10/7$. Since the height in the latter is the gradient of the position of a disordered elastic string, this shows that $ζ=5/4$ for a driven elastic string at depinning.
format Preprint
id arxiv_https___arxiv_org_abs_2302_13749
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Anchored advected interfaces, Oslo model, and roughness at depinning
Shapira, Assaf
Wiese, Kay Joerg
Disordered Systems and Neural Networks
Mathematical Physics
There is a plethora of 1-dimensional advected systems with an absorbing boundary: the Toom model of anchored interfaces, the directed exclusion process where in addition to diffusion particles and holes can jump over their right neighbor, simple diffusion with advection, and Oslo sandpiles. All these models share a roughness exponent of $ζ=1/4$, while the dynamic exponent $z$ varies, depending on the observable. We show that for the first three models $z=1$, $z=2$, and $z=1/2$ are realized, depending on the observable. The Oslo model is apart with a conjectured dynamic exponent of $z=10/7$. Since the height in the latter is the gradient of the position of a disordered elastic string, this shows that $ζ=5/4$ for a driven elastic string at depinning.
title Anchored advected interfaces, Oslo model, and roughness at depinning
topic Disordered Systems and Neural Networks
Mathematical Physics
url https://arxiv.org/abs/2302.13749