Continuous Move From BTW to Manna Model

TL;DR

This paper investigates how introducing anisotropy to the BTW model causes a crossover to Manna model behavior, revealing the relevance of perturbations at the fixed point and proposing a differential equation for the Green's function.

Contribution

It demonstrates the continuous transition from BTW to Manna models under anisotropic perturbation and introduces a differential equation fitting the Green's function of the system.

Findings

Crossover from BTW to Manna model observed with increasing anisotropy.

Infrared limit behavior aligns with the Manna model.

Proposed differential equation models the Green's function effectively.

Abstract

In the present paper we consider the BTW model perturbed by random-direction anisotropy with strength factor \epsilon ranging from 0 to 1 corresponding to BTW and Manna model receptively and investigate the properties of the statistical observables for various rates of anisotropy. By increasing the \epsilon, we observe a cross-over taking place between these models. For small length scales, the curves show properties similar to the BTW model whereas in the Infra red limit the corresponding \kappa is nearly the same as the Manna model. The observations confirm that this perturbation is relevant for the BTW fixed point and the infra red limit of the perturbed model is described by the Manna model. We also propose a differential equation whose solution properly fits with the the Green's function obtained by the simulation. This can help us to obtain the action of the perturbed model.