Kinetic Sectors and Nonequilibrium Dynamics in the δ-Ising Model
Abstract
We introduce and analyze the δ-Ising model, a kinetic Ising ferromagnet in which single-spin flips are accepted when their energy change does not exceed a tunable threshold. Varying the field and threshold opens or closes local flip channels, dividing parameter space into kinetic sectors, each governed by a fixed Markov transition operator. We prove that the dynamics retains global spin-inversion symmetry exactly when up and down spins have equal numbers of open channels. In one such sector on a periodic chain of length L, unbiased random initial states therefore reach the field-aligned and antifield states with probability 1/2 each. Closing a single channel leaves both states absorbing but makes the probability of ordering against the field decay as (2/π)L. Parameter sweeps correspond to ordered products of sector operators, which separate reaching a state from holding it, so hysteresis appears when a state is reached and released at different sector boundaries. We also show how increasing the system size can induce a Mpemba-like reversal, allowing a state with more misaligned spins to reach the final ordered state sooner on average. On a periodic chain, this reversal arises because the mean absorption time grows logarithmically with system size for many short domains but linearly for a single macroscopic domain, and it disappears when the bulk flip channel is opened. These findings show how a simple, intuitive rule for Ising dynamics links local kinetic constraints to field response, memory, and relaxation within a unified framework.
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BibTeX
@misc{cao2026kinetic,
title = {{Kinetic Sectors and Nonequilibrium Dynamics in the $δ$-Ising Model}},
author = {Dehen Cao and Wei Jiang and Ya Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36829},
eprint = {2610.36829},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36829},
}
RIS
TY - UNPB
TI - Kinetic Sectors and Nonequilibrium Dynamics in the δ-Ising Model
AU - Dehen Cao
AU - Wei Jiang
AU - Ya Zhang
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36829
UR - https://arxiv.org/abs/2610.36829
AB - We introduce and analyze the δ-Ising model, a kinetic Ising ferromagnet in which single-spin flips are accepted when their energy change does not exceed a tunable threshold. Varying the field and threshold opens or closes local flip channels, dividing parameter space into kinetic sectors, each governed by a fixed Markov transition operator. We prove that the dynamics retains global spin-inversion symmetry exactly when up and down spins have equal numbers of open channels. In one such sector on a periodic chain of length L, unbiased random initial states therefore reach the field-aligned and antifield states with probability 1/2 each. Closing a single channel leaves both states absorbing but makes the probability of ordering against the field decay as (2/π)^L. Parameter sweeps correspond to ordered products of sector operators, which separate reaching a state from holding it, so hysteresis appears when a state is reached and released at different sector boundaries. We also show how increasing the system size can induce a Mpemba-like reversal, allowing a state with more misaligned spins to reach the final ordered state sooner on average. On a periodic chain, this reversal arises because the mean absorption time grows logarithmically with system size for many short domains but linearly for a single macroscopic domain, and it disappears when the bulk flip channel is opened. These findings show how a simple, intuitive rule for Ising dynamics links local kinetic constraints to field response, memory, and relaxation within a unified framework.
ER -