Kavli Affiliate: Savdeep Sethi
| First 5 Authors: Gabriel Weiderpass, Mayur Sharma, Savdeep Sethi, ,
| Summary:
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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