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arXiv · 2410.23615

Solving the Kinetic Ising Model with Non-Reciprocity

Gabriel Artur Weiderpass·Mayur Sharma·Savdeep Sethi
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Abstract

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.

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Gabriel Artur Weiderpass, Mayur Sharma, Savdeep Sethi. 2024-10-31. Solving the Kinetic Ising Model with Non-Reciprocity. https://doi.org/10.1103/physreve.111.024107

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