Exact Hyperuniformity Exponents and Entropy Cusps in Models of Active-Absorbing Transition

TL;DR

This paper investigates the critical behavior of nonequilibrium phase transitions in 1D models, revealing hyperuniformity and entropy cusps at the transition point, with exact measures over absorbing states.

Contribution

It provides exact measures over absorbing states in 1D models and characterizes hyperuniformity and entropy behavior at the transition.

Findings

Both models exhibit hyperuniformity near the transition.

Configurational entropy shows a cusp at the transition point.

Exact measures over absorbing states are derived for the models.

Abstract

Recent studies of nonequilibrium phase transitions have shown that in many systems which have transitions involving an arrested phase, the arrested states show suppressed density fluctuations and a cusp in the configurational entropy at the transition point. We study quasistatic driving in the 1D fixed-energy abelian sandpile model, and in conserved lattice gases with range $n$ in 1D, and exactly determine the measure over the absorbing states for both cases, along with the behaviour of density fluctuations and the configurational entropy of absorbing states. We show that both models exhibit hyperuniformity near the transition, and also that the configurational entropy shows a cusp at the transition point in the conserved lattice gases.