Mean-field scaling function of the universality class of absorbing phase transitions with a conserved field

TL;DR

This paper analytically derives the universal mean-field scaling function for absorbing phase transitions with a conserved field, confirming four as the upper critical dimension through comparison with high-dimensional numerical data.

Contribution

It provides the first analytical derivation of the universal mean-field scaling function for this universality class, validating numerical results and identifying the upper critical dimension.

Findings

Universal mean-field scaling function derived analytically.

Confirmation that four is the upper critical dimension.

Excellent agreement with high-dimensional numerical data.

Abstract

We consider two mean-field like models which belong to the universality class of absorbing phase transitions with a conserved field. In both cases we derive analytically the order parameter as function of the control parameter and of an external field conjugated to the order parameter. This allows us to calculate the universal scaling function of the mean-field behavior. The obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models, showing that four is the upper critical dimension of this particular universality class.