English

Results and conjectures on a toy model of depinning

Mathematical Physics 2020-05-21 v1 math.MP

Abstract

We review recent results and conjectures for a simplified version of the depinning problem in presence of disorder which was introduced by Derrida and Retaux in 2014. For this toy model, the depinning transition has been predicted to be of the Berezinskii--Kosterlitz--Thouless type. Here we discuss under which integrability conditions this prediction can be proved and how it is modified otherwise.

Keywords

Cite

@article{arxiv.2005.10208,
  title  = {Results and conjectures on a toy model of depinning},
  author = {Bernard Derrida and Zhan Shi},
  journal= {arXiv preprint arXiv:2005.10208},
  year   = {2020}
}

Comments

Sumitted to the Moscow Mathematical Journal for the volume dedicated to the memory of Roland Dobrushin