Universal finite-size scaling behavior and universal dynamical scaling behavior of absorbing phase transitions with a conserved field

TL;DR

This paper investigates the finite-size and dynamical scaling behaviors of absorbing phase transitions with a conserved field, validating hyperscaling relations and connecting avalanche exponents to ordinary critical exponents.

Contribution

It provides a numerical analysis of three models, accurately determines critical exponents, and links avalanche exponents to continuous phase transition exponents through hyperscaling.

Findings

Validated hyperscaling relations for absorbing phase transitions

Connected avalanche exponents to ordinary critical exponents

Demonstrated universal finite-size and dynamical scaling behaviors

Abstract

We analyze numerically three different models exhibiting an absorbing phase transition. We focus on the finite-size scaling as well as the dynamical scaling behavior. An accurate determination of several critical exponents allows to validate certain hyperscaling relations. Using this hyperscaling relations it is possible to express the avalanche exponents of a self-organized critical system in terms of the ordinary exponents of a continuous absorbing phase transition.