High-Precision Simulations of the Parity Conserving Directed Percolation Universality Class in 1+1 Dimensions

TL;DR

This paper presents high-precision simulations of the parity conserving directed percolation class in 1+1 dimensions, revealing that several critical exponents are exactly rational numbers, especially with the order parameter exponent being precisely 1.

Contribution

The study provides the most accurate estimates of critical exponents for pcDP, confirming some as exact rational numbers and clarifying previous uncertainties about the order parameter exponent.

Findings

Critical exponents close to simple rational numbers.

Order parameter exponent $eta$ is exactly 1.

Distinct scaling behaviors in even and odd sectors.

Abstract

Next to the directed percolation (DP) universality class, parity conserving directed percolation (pcDP; also called parity conserving branching annihilating random walks, pcBARW) is the second-most important model with an absorbing state transition. Its distinction from ordinary DP is that particle number is conserved modulo 2, which implies that there are two distinct sectors in systems with a finite initial number of particles: Realizations with even and odd particle numbers show different scaling behaviors, and systems in the odd sector cannot die. An intriguing feature of pcDP it is that some of its critical exponents seem to be very simple rational numbers. The most prominent is the one describing the average number of particles (or active sites) in the even sector, which is asymptotically constant. In contrast, the dynamical critical exponent (which is the same in both sectors) seems not close to any simple rational. Finally, the order parameter exponent $\beta$ (which is also the same in both sectors) is, according to the most precise previous simulations, rather close to 1, but incompatible with it. We present high statistics simulations which clarify this situation, and which indicate several other intriguing properties of pcPD clusters. In particular, we find that all exponents which were close to rationals are even closer, and $\beta = 1.000$ with the error in the next digit.