Driving, conservation and absorbing states in sandpiles

TL;DR

This paper compares driven dissipative sandpiles with fixed-energy models using a phenomenological field theory, revealing different approaches to criticality and providing critical exponent calculations supported by simulations.

Contribution

It introduces a field theory framework that captures symmetries and conservation laws, highlighting differences in critical behavior between driven and fixed-energy sandpile models.

Findings

Fixed-energy model has an absorbing-state phase transition at d_c=4

Driven model approaches criticality differently from fixed-energy models

Numerical simulations support theoretical critical exponent predictions

Abstract

We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding fixed-energy model. The latter displays an absorbing-state phase transition with upper critical dimension $d_c=4$. We show that the driven model exhibits a fundamentally different approach to the critical point, and compute a subset of critical exponents. We present numerical simulations in support of our theoretical predictions.