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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2512.02241 |
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| _version_ | 1866915674416218112 |
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| author | Grassberger, Peter |
| author_facet | Grassberger, Peter |
| contents | 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 $β$ (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 $β= 1.000$ with the error in the next digit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_02241 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High-Precision Simulations of the Parity Conserving Directed Percolation Universality Class in 1+1 Dimensions Grassberger, Peter Statistical Mechanics 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 $β$ (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 $β= 1.000$ with the error in the next digit. |
| title | High-Precision Simulations of the Parity Conserving Directed Percolation Universality Class in 1+1 Dimensions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.02241 |