An Exact Solution for the Kinetic Ising Model with Non-Reciprocity

Gabriel Weiderpass; Mayur Sharma; Savdeep Sethi

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arXiv · 2411.00059

An Exact Solution for the Kinetic Ising Model with Non-Reciprocity

Gabriel Weiderpass·Mayur Sharma·Savdeep Sethi

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Abstract

A wide range of non-equilibrium phenomena in nature involve non-reciprocal interactions. To understand the novel behaviors that can emerge in such systems, finding tractable models is essential. With this goal, we introduce a non-reciprocal generalization of the kinetic Ising model in one dimension and solve it exactly. Our solution uncovers novel properties driven by non-reciprocity, such as underdamped phases, critically damped phases where a system of size $N$ is described by an $N^{th}$-order exceptional point, and wave phenomena influenced by the parity of $N$. Additionally, we examine the low-energy behavior of these systems in various limits, demonstrating that non-reciprocity leads to unique scaling behavior at zero temperature.

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cond-mat.stat-mech cond-mat.soft hep-th nlin.SI

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Gabriel Weiderpass, Mayur Sharma, Savdeep Sethi. 2024-10-31. An Exact Solution for the Kinetic Ising Model with Non-Reciprocity. https://arxiv.org/abs/2411.00059

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