Connecting the Micro-dynamics to the Emergent Macro-variables: Self-Organized Criticality and Absorbing Phase Transitions in the Deterministic Lattice Gas

TL;DR

This paper reexamines the Deterministic Lattice Gas model, revealing its connection to self-organized criticality and classifying it within the Manna universality class of absorbing phase transitions, contrary to previous expectations.

Contribution

It demonstrates that the deterministic lattice gas belongs to the Manna universality class, linking microscopic dynamics to macroscopic critical phenomena in a novel way.

Findings

Density fluctuations depend on system size and relate to Langevin equations.

The model exhibits critical behavior at the absorbing state phase transition.

It is the first fully deterministic model in the Manna universality class.

Abstract

We reinvestigate the Deterministic Lattice Gas introduced as a paradigmatic model of the 1/f spectra (Phys. Rev. Lett. V26, 3103 (1990)) arising according to the Self-Organized Criticality scenario. We demonstrate that the density fluctuations exhibit an unexpected dependence on systems size and relate the finding to effective Langevin equations. The low density behavior is controlled by the critical properties of the gas at the absorbing state phase transition. We also show that the Deterministic Lattice Gas is in the Manna universality class of absorbing state phase transitions. This is in contrast to expectations in the literature which suggested that the entirely deterministic nature of the dynamics would put the model in a different universality class. To our knowledge this is the first fully deterministic member of the Manna universality class.