Universality in self-organized critical slope models

TL;DR

This paper investigates the critical behavior of self-organized critical slope models, revealing their unique universality class and providing a comprehensive set of scaling exponents through analytical solutions and comparisons with simulations.

Contribution

It introduces a complete analytical solution for the critical slope models and identifies their distinct universality class, differentiating them from other depinning models.

Findings

Complete set of scaling exponents derived

Model belongs to a different universality class than constant force depinning models

Two universality classes identified: random and periodic pinning

Abstract

The dynamics of critical slope self-organized critical models is studied, using a previous mapping into a linear interface depinning model dragged at one end. The model is solved obtaining the complete set of scaling exponents. Some results are supported by previous RG developed for constant force linear interface depinning models but others, like the linear dependency of the susceptibility with system size, are intrinsic of this model which belongs to a different universality class. The comparison of our results with numerical simulations of ricepile and vortexpile models reported in the literature reveals that, as in the constant force case, there are two universality classes corresponding to random and periodic pinning.