Novel Transition to fully absorbing state without long-range spatial order in Directed Percolation class

TL;DR

This paper investigates a transition in coupled Gauss maps to a band periodic state without long-range order, demonstrating that the critical behavior aligns with the directed percolation universality class.

Contribution

It identifies a DP-class transition in a system with no long-range spatial order, expanding understanding of DP universality beyond traditional spatially ordered systems.

Findings

Critical exponents match 1D DP class

Power-law decay of flipping rate at criticality

Excellent finite-size and off-critical scaling observed

Abstract

We study coupled Gauss maps in one dimension and observe a transition to band periodic state with 2 bands. This is a periodic state with period-2 in a coarse-grained sense. This state does not show any long-range order in space. We compute two different order parameters to quantify the transition a) Flipping rate $F(t)$ which measures departures from period-2 and b) Persistence $P(t)$ which quantifies the loss of memory of initial conditions. At the critical point, $F(t)$ shows a power-law decay with exponent 0.158 which is close to 1-D directed percolation (DP) transition. The persistence exponent at the critical point is found to be 1.51 which matches with several models in 1-D DP class. We also study the finite-size scaling and off-critical scaling to estimate other exponents $z$ and $\nu_{\parallel}$. We observe excellent scaling for both $F(t)$ as well as $P(t)$ and the exponents obtained are clearly in DP class. We believe that DP transition could be observed in systems where activity goes to zero even if the spatial profile could be inhomogeneous and lacking any long-range order.