Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23615 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915220089208832 |
|---|---|
| author | Weiderpass, Gabriel Artur Sharma, Mayur Sethi, Savdeep |
| author_facet | Weiderpass, Gabriel Artur Sharma, Mayur Sethi, Savdeep |
| contents | Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for infinite, semi-infinite and finite systems with either periodic or open boundary conditions. The exact solution allows us to explore a range of novel phenomena tied to non-reciprocity like non-reciprocity induced frustration and wave phenomena with interesting parity-dependence for finite systems of size $N$.
We study dynamical questions like the approach to equilibrium with various boundary conditions. We find new regimes, separated by $N^{th}$-order exceptional points, which can be classified as overdamped, underdamped and critically damped phases. Despite these new regimes, long-time order is only present at zero temperature. Additionally, we explore the low-energy behavior of the system in various limits, including the ageing and spatio-temporal Porod regimes, demonstrating that non-reciprocity induces unique scaling behavior at zero temperature. Lastly, we present general results for systems where spins interact with no more than two spins, outlining the conditions under which long-time order may exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23615 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solving the Kinetic Ising Model with Non-Reciprocity Weiderpass, Gabriel Artur Sharma, Mayur Sethi, Savdeep Statistical Mechanics Soft Condensed Matter High Energy Physics - Theory Exactly Solvable and Integrable Systems Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for infinite, semi-infinite and finite systems with either periodic or open boundary conditions. The exact solution allows us to explore a range of novel phenomena tied to non-reciprocity like non-reciprocity induced frustration and wave phenomena with interesting parity-dependence for finite systems of size $N$. We study dynamical questions like the approach to equilibrium with various boundary conditions. We find new regimes, separated by $N^{th}$-order exceptional points, which can be classified as overdamped, underdamped and critically damped phases. Despite these new regimes, long-time order is only present at zero temperature. Additionally, we explore the low-energy behavior of the system in various limits, including the ageing and spatio-temporal Porod regimes, demonstrating that non-reciprocity induces unique scaling behavior at zero temperature. Lastly, we present general results for systems where spins interact with no more than two spins, outlining the conditions under which long-time order may exist. |
| title | Solving the Kinetic Ising Model with Non-Reciprocity |
| topic | Statistical Mechanics Soft Condensed Matter High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2410.23615 |