The average avalanche size in the Manna Model and other models of self-organised criticality

TL;DR

This paper provides exact calculations of the average avalanche size in models of self-organised criticality, highlighting the analytical methods and their connection to field theory, with implications for higher-dimensional and boundary condition variations.

Contribution

It offers analytical expressions for average avalanche sizes in SOC models, extending understanding beyond one dimension and linking to field theory approaches.

Findings

Exact average avalanche size formulas derived

Analytical references provided for numerical validation

Connection established between avalanche calculations and field theory

Abstract

The average avalanche size can be calculated exactly in a number of models of self-organised criticality (SOC). While the calculation is straight-forward in one dimension, it is more involved in higher dimensions and further complicated by the presence of different boundary conditions and different forms of external driving. Amplitudes of the leading order are determined analytically and evaluated to obtain analytical references for numerical work. A subtle link exists between the procedure to calculate the average avalanche size and the field theory of SOC.