Solving the Kinetic Ising Model with Non-Reciprocity
arXiv:2410.23615 · doi:10.1103/PhysRevE.111.024107
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 . We study dynamical questions like the approach to equilibrium with various boundary conditions. We find new regimes, separated by -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.
74 pages, LaTeX, 13 figures; published version with additional comments and references
References in corpus (49)
- Exceptional Topology of Non-Hermitian Systems
- Non-Hermitian Physics
- Hierarchical group dynamics in pigeon flocks
- Observation of bulk boundary correspondence breakdown in topolectrical circuits
- Non-reciprocal phase transitions
- Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
- Nonreciprocal Photon Transmission and Amplification via Reservoir Engineering
- Non-reciprocal robotic metamaterials
- Topological active matter
- Odd elasticity
- Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
- Odd dynamics of living chiral crystals
- Nonreciprocity as a generic route to traveling states
- Odd Viscosity and Odd Elasticity
- Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics
- Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
- Statistical mechanics for non-reciprocal forces
- Scalar Active Mixtures: The Non-Reciprocal Cahn-Hilliard Model
- Non-Hermitian band topology and skin modes in active elastic media
- Irreversibility, heat and information flows induced by non-reciprocal interactions
- Non-reciprocity across scales in active mixtures
- Non-reciprocal topological solitons in active metamaterials
- Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions
- Aging, phase ordering and conformal invariance
- Active topolectrical circuits
- Non-Hermitian Localization in Biological Networks
- Non-Hermitian phase transition from a polariton Bose-Einstein condensate to a photon laser
- Critical fluctuations at a many-body exceptional point
- Nonreciprocal pattern formation of conserved fields
- Collective Motion with Anticipation: Flocking, Spinning, and Swarming
- Kuramoto model for excitation-inhibition-based oscillations
- The non-reciprocal Dicke model
- Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation
- Active nonreciprocal attraction between motile particles in an elastic medium
- Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
- Introduction to quantum non-reciprocal interactions: from non-Hermitian Hamiltonians to quantum master equations and quantum feedforward schemes
- Non-reciprocal frustration: time crystalline order-by-disorder phenomenon and a spin-glass-like state
- A unifying framework for mean-field theories of asymmetric kinetic Ising systems
- Nonequilibrium Stationary States and Phase Transitions in Directed Ising Models
- Sampling efficiency of transverse forces in dense liquids
- Dynamics of the directed Ising chain
- Controlled asymmetric Ising model implemented with parametric micromechanical oscillators
- Rates for irreversible Gibbsian Ising models
- Dynamics of the two-dimensional directed Ising model in the paramagnetic phase
- Freezing in stripe states for kinetic Ising models: a comparative study of three dynamics
- Non-reciprocal interactions spatially propagate fluctuations in a 2D Ising model
- Non-reciprocal Phase Separations with Non-conserved Order Parameters
- Dynamics of the two-dimensional directed Ising model: zero-temperature coarsening
- Generic phase coexistence in the totally asymmetric kinetic Ising model