Exact solution of the Glauber-Ising model on the finite-length semi-open chain

Abstract

The exact time-space correlation function of the $1D$ Glauber-Ising model, quenched to temperature $T=0$ and on a semi-open lattice of finite size $N$, is obtained. This also allows to deduce the exact empty-interval probability of the dual $1D$ coagulation-diffusion process on a periodic finite ring and to reproduce the long-time decay of the particle concentration. These results are consistent with the generic expectations of dynamical finite-size scaling theory.

arXiv commentLatex2e, 1+23 pp, 4 figures included, final form

References in corpus (37)

• Theory of Phase Ordering Kinetics
• Phase transitions in an exactly soluble one-dimensional exclusion process
• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Response of non-equilibrium systems at criticality: Exact results for the Glauber-Ising chain
• Fluctuation dissipation ratio in the one dimensional kinetic Ising model
• Glauber slow dynamics of the magnetization in a molecular Ising chain
• The Energy-Scaling Approach to Phase-Ordering Growth Laws
• Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
• Aging in the long-range Ising model
• Modified fluctuation-dissipation theorem near non-equilibrium states and applications to the Glauber-Ising chain
• General Solutions for Multispin Two-Time Correlation and Response Functions in the Glauber-Ising Chain
• On the universality of the fluctuation-dissipation ratio in non-equilibrium critical dynamics
• The duality relation between Glauber dynamics and the diffusion-annihilation model as a similarity transformation
• One dimensional phase-ordering in the Ising model with space decaying interactions
• Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input
• Dynamic Matrix Ansatz for Integrable Reaction-Diffusion Processes
• Phase transition of the one-dimensional coagulation-production process
• Zero-Temperature Coarsening in the Two-Dimensional Long-Range Ising Model
• Universality in the time correlations of the long-range 1d Ising model
• Finite-Size Scaling Studies of Reaction-Diffusion Systems Part III: Numerical Methods
• Dynamic Heterogeneity in the Glauber-Ising chain
• Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method
• Effect of antiferromagnetic exchange interactions on the Glauber dynamics of one-dimensional Ising models
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model
• Non-universality of aging during phase separation of the two-dimensional long-range Ising model
• Physical ageing from generalised time-translation-invariance
• Dynamics of Ising models near zero temperature : Real Space Renormalization Approach
• Non-equilibrium relaxations: ageing and finite-size effects
• The Glauber-Ising chain under low-temperature protocols
• Crossover properties of a one-dimensional reaction-diffusion process with a transport current
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process
• Aging processes in reversible reaction-diffusion systems: Monte Carlo simulations
• Reaction-diffusion on the fully-connected lattice: $A+A\to A$
• Rigorous lower bound of the dynamical critical exponent of the Ising model
• Emergent Hydrodynamics in an Exclusion Process with Long-Range Interactions