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An Absorbing State Model with an Emergent Ising Transition
Abstract
We study a dynamical model of repulsive needles with centers fixed on a square lattice. Needles that overlap are active and receive a repulsive rotation $ θ\in [0,ε)$; needles with no overlap do not move. This model exhibits an absorbing state transition. Nematic order was observed for long needles. For a range of needle lengths and ε, the system self-organizes into a state with checkerboard symmetry. As ε is increased, this phase melts and becomes disordered. Remarkably, we find that this phase boundary exhibits critical exponents identical to those of the equilibrium 2D Ising model.
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BibTeX
@misc{ai2026absorbing,
title = {{An Absorbing State Model with an Emergent Ising Transition}},
author = {Shen Ai and Dov Levine and Paul Chaikin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03936},
eprint = {2610.03936},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03936},
}
RIS
TY - UNPB
TI - An Absorbing State Model with an Emergent Ising Transition
AU - Shen Ai
AU - Dov Levine
AU - Paul Chaikin
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03936
UR - https://arxiv.org/abs/2610.03936
AB - We study a dynamical model of repulsive needles with centers fixed on a square lattice. Needles that overlap are active and receive a repulsive rotation $ θ\in [0,ε)$; needles with no overlap do not move. This model exhibits an absorbing state transition. Nematic order was observed for long needles. For a range of needle lengths and ε, the system self-organizes into a state with checkerboard symmetry. As ε is increased, this phase melts and becomes disordered. Remarkably, we find that this phase boundary exhibits critical exponents identical to those of the equilibrium 2D Ising model.
ER -